Solving Word Questions
With LOTS of examples!
In Algebra we often have word questions like:
![](http://himalayanshop.online/777/templates/cheerup/res/banner1.gif)
Example: Sam and Alex play tennis.
On the weekend Sam played 4 more games than Alex did, and together they played 12 games.
How many games did Alex play?
How do we solve them?
The trick is to break the solution into two parts:
Turn the English into Algebra.
Then use Algebra to solve.
Turning English into Algebra
To turn the English into Algebra it helps to:
- Read the whole thing first
- Do a sketch if possible
- Assign letters for the values
- Find or work out formulas
You should also write down what is actually being asked for , so you know where you are going and when you have arrived!
Also look for key words:
Thinking Clearly
Some wording can be tricky, making it hard to think "the right way around", such as:
Example: Sam has 2 dollars less than Alex. How do we write this as an equation?
- Let S = dollars Sam has
- Let A = dollars Alex has
Now ... is that: S − 2 = A
or should it be: S = A − 2
or should it be: S = 2 − A
The correct answer is S = A − 2
( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")
Example: on our street there are twice as many dogs as cats. How do we write this as an equation?
- Let D = number of dogs
- Let C = number of cats
Now ... is that: 2D = C
or should it be: D = 2C
Think carefully now!
The correct answer is D = 2C
( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")
Let's start with a really simple example so we see how it's done:
Example: A rectangular garden is 12m by 5m, what is its area ?
Turn the English into Algebra:
- Use w for width of rectangle: w = 12m
- Use h for height of rectangle: h = 5m
Formula for Area of a Rectangle : A = w × h
We are being asked for the Area.
A = w × h = 12 × 5 = 60 m 2
The area is 60 square meters .
Now let's try the example from the top of the page:
![maths problem solving word questions tennis](https://www.mathsisfun.com/images/tennis.jpg)
Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?
- Use S for how many games Sam played
- Use A for how many games Alex played
We know that Sam played 4 more games than Alex, so: S = A + 4
And we know that together they played 12 games: S + A = 12
We are being asked for how many games Alex played: A
Which means that Alex played 4 games of tennis.
Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!
A slightly harder example:
![maths problem solving word questions table](https://www.mathsisfun.com/images/table.jpg)
Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?
- Use a for Alex's work rate
- Use s for Sam's work rate
12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10
30 days of Alex alone is also 10 tables: 30a = 10
We are being asked how long it would take Sam to make 10 tables.
30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3
Which means that Sam's rate is half a table a day (faster than Alex!)
So 10 tables would take Sam just 20 days.
Should Sam be paid more I wonder?
And another "substitution" example:
![maths problem solving word questions track](https://www.mathsisfun.com/images/track.jpg)
Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?
- The number of "5 hour" days: d
- The number of "3 hour" days: e
We know there are seven days in the week, so: d + e = 7
And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27
We are being asked for how many days she trains for 5 hours: d
The number of "5 hour" days is 3
Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.
3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours
Some examples from Geometry:
Example: A circle has an area of 12 mm 2 , what is its radius?
- Use A for Area: A = 12 mm 2
- Use r for radius
And the formula for Area is: A = π r 2
We are being asked for the radius.
We need to rearrange the formula to find the area
Example: A cube has a volume of 125 mm 3 , what is its surface area?
Make a quick sketch:
- Use V for Volume
- Use A for Area
- Use s for side length of cube
- Volume of a cube: V = s 3
- Surface area of a cube: A = 6s 2
We are being asked for the surface area.
First work out s using the volume formula:
Now we can calculate surface area:
An example about Money:
![maths problem solving word questions pizza](https://www.mathsisfun.com/images/pizza.jpg)
Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?
- Joel's normal rate of pay: $N per hour
- Joel works for 40 hours at $N per hour = $40N
- When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
- Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
- And together he earned $660, so:
$40N + $(12 × 1¼N) = $660
We are being asked for Joel's normal rate of pay $N.
So Joel’s normal rate of pay is $12 per hour
Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660
More about Money, with these two examples involving Compound Interest
Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?
This is the compound interest formula:
So we will use these letters:
- Present Value PV = $2,000
- Interest Rate (as a decimal): r = 0.11
- Number of Periods: n = 3
- Future Value (the value we want): FV
We are being asked for the Future Value: FV
Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?
The compound interest formula:
- Present Value PV = $1,000
- Interest Rate (the value we want): r
- Number of Periods: n = 9
- Future Value: FV = $1,551.33
We are being asked for the Interest Rate: r
So the annual rate of interest is 5%
Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33
And an example of a Ratio question:
Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?
- Number of boys now: b
- Number of girls now: g
The current ratio is 4 : 3
Which can be rearranged to 3b = 4g
At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1
b + 4 g − 2 = 2 1
Which can be rearranged to b + 4 = 2(g − 2)
We are being asked for how many students there are altogether now: b + g
There are 12 girls !
And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys
So there are now 12 girls and 16 boys in the class, making 28 students altogether .
There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1
And now for some Quadratic Equations :
Example: The product of two consecutive even integers is 168. What are the integers?
Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.
We will call the smaller integer n , and so the larger integer must be n+2
And we are told the product (what we get after multiplying) is 168, so we know:
n(n + 2) = 168
We are being asked for the integers
That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.
Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES
Check 12: 12(12 + 2) = 12×14 = 168 YES
So there are two solutions: −14 and −12 is one, 12 and 14 is the other.
Note: we could have also tried "guess and check":
- We could try, say, n=10: 10(12) = 120 NO (too small)
- Next we could try n=12: 12(14) = 168 YES
But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).
Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?
Let's first make a sketch so we get things right!:
- the length of the room: L
- the width of the room: W
- the total Area including veranda: A
- the width of the room is half its length: W = ½L
- the total area is the (room width + 3) times the length: A = (W+3) × L = 56
We are being asked for the length of the room: L
This is a quadratic equation , there are many ways to solve it, this time let's use factoring :
And so L = 8 or −14
There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!
So the length of the room is 8 m
L = 8, so W = ½L = 4
So the area of the rectangle = (W+3) × L = 7 × 8 = 56
There we are ...
... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?
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120 Math Word Problems To Challenge Students Grades 1 to 8
![maths problem solving word questions no image](https://images.prismic.io/prodigy-website/655d9c7b-5a70-4b74-b4ed-2cf894c15951_math-word-problems-blog-header.jpg?auto=compress%2Cformat&rect=0%2C354%2C2121%2C707&w=1920&h=640&fit=max)
Written by Marcus Guido
Hey teachers! 👋
Use Prodigy to spark a love for math in your students – including when solving word problems!
- Teaching Tools
- Subtraction
- Multiplication
- Mixed operations
- Ordering and number sense
- Comparing and sequencing
- Physical measurement
- Ratios and percentages
- Probability and data relationships
You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.
A jolt of creativity would help. But it doesn’t come.
Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.
This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.
There are 120 examples in total.
The list of examples is supplemented by tips to create engaging and challenging math word problems.
120 Math word problems, categorized by skill
Addition word problems.
![maths problem solving word questions A teacher is teaching three students with a whiteboard happily.](https://images.prismic.io/prodigy-website/912dbd61-e484-48b4-bde1-63b80417f327_2017-01-09-Math-Whiteboard-condensed-5.jpeg?auto=compress%2Cformat&fit=max&w=600&h=400)
Best for: 1st grade, 2nd grade
1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?
2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?
3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?
5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?
6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?
7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?
8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?
Subtraction word problems
Best for: 1st grade, second grade
9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?
10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?
11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
![maths problem solving word questions Five middle school students sitting at a row of desks playing Prodigy Math on tablets.](https://images.prismic.io/prodigy-website/34aacb6e-d6e5-4b04-b5b3-5584748ed6b2_kids_using_prodigy_edited.jpeg?auto=compress%2Cformat&fit=max&w=555&h=611)
Practice math word problems with Prodigy Math
Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!
12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?
13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?
14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?
15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?
16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?
Multiplication word problems
![maths problem solving word questions A hand holding a pen is doing calculation on a pice of papper](https://images.prismic.io/prodigy-website/23ae7371-4b93-4eeb-850f-b123bd8f7a94_2016-12-22-Student-Practicing-Multiplication-condensed-3.jpeg?auto=compress%2Cformat&fit=max&w=600&h=463)
Best for: 2nd grade, 3rd grade
17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?
18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?
19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?
20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?
21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?
Division word problems
Best for: 3rd grade, 4th grade, 5th grade
22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?
23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?
24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?
25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?
26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?
Mixed operations word problems
![maths problem solving word questions A female teacher is instructing student math on a blackboard](https://images.prismic.io/prodigy-website/ba8c1b02-71df-4066-8d2b-f9802ff555bd_2017-04-28-Students-at-Blackboard-with-Teacher-condensed-1.jpeg?auto=compress%2Cformat&fit=max&w=600&h=400)
27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?
28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?
29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?
30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?
Ordering and number sense word problems
31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?
32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?
33. Composing Numbers: What number is 6 tens and 10 ones?
34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?
35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?
Fractions word problems
![maths problem solving word questions A student is drawing on a notebook, holding a pencil.](https://images.prismic.io/prodigy-website/2ead360b-740e-4a22-94f1-dd83c61432fa_2017-03-15-Student-Taking-Notes-on-Graph-Paper-condensed-2.jpeg?auto=compress%2Cformat&fit=max&w=600&h=400)
Best for: 3rd grade, 4th grade, 5th grade, 6th grade
36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?
37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?
38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?
39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?
40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?
41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?
42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?
43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?
44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.
45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?
46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.
Decimals word problems
Best for: 4th grade, 5th grade
47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?
48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?
49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?
50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?
51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?
52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?
Comparing and sequencing word problems
![maths problem solving word questions Four students are sitting together and discussing math questions](https://images.prismic.io/prodigy-website/4dd8b19c-0b8c-4b30-a5e1-7c31a4128604_2016-12-15-Students-Working-Together-condensed-4.jpeg?auto=compress%2Cformat&fit=max&w=600&h=400)
Best for: Kindergarten, 1st grade, 2nd grade
53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?
54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?
55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?
56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?
57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?
58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?
59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?
Time word problems
66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?
69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?
70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?
71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?
Money word problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade
60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?
61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?
62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?
63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?
64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?
65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?
67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.
68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?
Physical measurement word problems
![maths problem solving word questions A girl is doing math practice](https://images.prismic.io/prodigy-website/8cd19f94-2065-43ee-b941-9a6691fdc43a_2017-03-09-Young-Female-Student-Writing-Test-condensed-2.jpeg?auto=compress%2Cformat&fit=max&w=600&h=400)
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade
72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?
73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?
74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?
75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?
![maths problem solving word questions A tablet showing an example of Prodigy Math's battle gameplay.](https://images.prismic.io/prodigy-website/913d1283-73b4-4902-bc57-1fc906ff4e66_about-us-game-682x640.png?auto=compress%2Cformat&fit=max&w=682&h=640)
76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?
77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?
78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?
79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?
80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?
81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?
Ratios and percentages word problems
Best for: 4th grade, 5th grade, 6th grade
82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?
83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?
84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?
85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?
86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?
87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?
88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?
Probability and data relationships word problems
![maths problem solving word questions Two students are calculating on a whiteboard](https://images.prismic.io/prodigy-website/a6ed6200-25df-4c61-86e9-5079f52eebb3_2017-03-09-Math-on-Whiteboard-condensed-3.jpeg?auto=compress%2Cformat&fit=max&w=600&h=400)
Best for: 4th grade, 5th grade, 6th grade, 7th grade
89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?
90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?
91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.
92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?
93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?
94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?
95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .
Geometry word problems
Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade
96. Introducing Perimeter: The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?
97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?
98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?
99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?
100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?
101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?
102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?
103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?
104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?
105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?
106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?
107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?
108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?
109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?
110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?
111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?
112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?
113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?
114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?
Variables word problems
![maths problem solving word questions A hand is calculating math problem on a blacboard](https://images.prismic.io/prodigy-website/5388766b-c3c4-49d5-80fd-91f6ddfffbdb_2017-03-09-Math-Equations-on-Chalkboard-condensed.jpeg?auto=compress%2Cformat&fit=max&w=600&h=400)
Best for: 6th grade, 7th grade, 8th grade
115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?
116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.
117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.
118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.
119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.
120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?
How to easily make your own math word problems & word problems worksheets
![maths problem solving word questions Two teachers are discussing math with a pen and a notebook](https://images.prismic.io/prodigy-website/8acb8e8c-c78c-4a6f-bfb5-fbb55bc85565_2017-06-01-Teacher-Meeting-condensed-1.jpeg?auto=compress%2Cformat&fit=max&w=600&h=401)
Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:
- Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.
A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.
Final thoughts about math word problems
You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.
Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.
The result?
A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.
Math Word Problems
Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.
There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:
- Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
- Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
- Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
- Calculate : Use your strategy to solve the problem.
- Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.
Most Popular Math Word Problems this Week
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- \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
- \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
- \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
- \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
- \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
- How do you solve word problems?
- To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
- How do you identify word problems in math?
- Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
- Is there a calculator that can solve word problems?
- Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
- What is an age problem?
- An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.
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Math Word Problem Worksheets
Read, explore, and solve over 1000 math word problems based on addition, subtraction, multiplication, division, fraction, decimal, ratio and more. These word problems help children hone their reading and analytical skills; understand the real-life application of math operations and other math topics. Print our exclusive colorful theme-based worksheets for a fun-filled teaching experience! Use the answer key provided below each worksheet to assist children in verifying their solutions.
List of Word Problem Worksheets
Explore the word problem worksheets in detail.
Addition Word Problems
Have 'total' fun by adding up a wide range of addends displayed in these worksheets! Simple real-life scenarios form the basis of these addition word problem worksheets.
Subtraction Word Problems
Learning can be a huge 'take away'! Find the difference between the numbers provided in each subtraction word problem. Large number subtraction up to six-digits can also be found here.
Addition and Subtraction Word Problems
Bring on 'A' game with our addition and subtraction word problems! Read, analyze, and solve real-life scenarios based on adding and subtracting numbers as required.
Multiplication Word Problems
Get 'product'ive with over 100 highly engaging multiplication word problems! Find the product and use the answer key to verify your solution. Free worksheets are also available.
Division Word Problems
"Divide and conquer" this huge collection of division word problems. Exclusive worksheets are available for the division problem leaving no remainder and with the remainder.
Fraction Word Problems
Perform various mathematical operations to solve the umpteen number of word problems based on like and unlike fractions, proper and improper fractions, and mixed numbers.
Decimal Word Problems
Let's get to the 'point'! Add, subtract, multiply, and divide to solve these decimal word problems. A wide selection of printable worksheets is available in this section. Use the answer key to verify your answers.
Ratio Word problems
Double up your success ratio with these sets of word problems, which cover a multitude of topics like express in the ratio, reducing the ratio, part-to-part ratio, part-to-whole ratio and more.
Venn Diagram Word Problems - Two Sets
Help your children improve their data analysis skills with these well-researched Venn diagram word problem worksheets. Find the union, intersection, complement and difference of two sets.
Venn Diagram Word Problems - Three Sets
These Venn diagram word problems provide ample practice in real-life application of Venn diagram involving three sets. The worksheets containing the universal set are also included.
Equation Word Problems
The printable worksheets here feature exercises consisting of one-step, two-step and multi-step equation word problems involving fractions, decimals and integers. MCQs to test the knowledge acquired have also been included.
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Free Printable Math Word Problems worksheets
Math Word Problems: Discover a vast collection of free printable worksheets, covering various topics and difficulty levels, to help students enhance their problem-solving skills and mathematical understanding.
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Math Word Problems worksheets are an essential tool for teachers to help their students develop strong problem-solving skills and a deep understanding of mathematical concepts. These worksheets cover a wide range of topics, from basic arithmetic to advanced algebra, and are designed to challenge students at every grade level. Teachers can use these worksheets to supplement their existing curriculum, provide extra practice for struggling students, or as a fun and engaging activity for the whole class. With a variety of formats and difficulty levels, Math Word Problems worksheets are an invaluable resource for educators looking to improve their students' mathematical abilities and prepare them for success in the classroom and beyond.
Quizizz is an innovative platform that offers a wide range of educational resources, including Math Word Problems worksheets, to help teachers create engaging and interactive learning experiences for their students. With Quizizz, educators can easily find and customize worksheets to fit their specific needs, as well as track student progress and provide instant feedback. In addition to Math Word Problems worksheets, Quizizz also offers a variety of other tools and resources, such as quizzes, flashcards, and interactive games, to help teachers create a comprehensive and engaging learning environment. By incorporating Quizizz into their lesson plans, teachers can ensure that their students are not only mastering essential math skills but also developing a love for learning and a strong foundation for future success.
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Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.
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Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.
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Math Word Problem Solutions
Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.
Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?
Simplified Equation: 17 - x = 8
Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?
Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)
Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}
Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?
Simplified: 40 - 10 - 5
Pre-Algebra Solutions
Below are examples of Pre-Algebra math problems that can be solved.
- Variables, Expressions, and Integers
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Below are examples of Trigonometry math problems that can be solved.
- Algebra Concepts and Expressions Review
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- Simplifying Trigonometric Expressions
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- Complex Numbers
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- Exponential and Logarithmic Functions
- Vector Arithmetic
Precalculus Solutions
Below are examples of Precalculus math problems that can be solved.
- Operations on Functions
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- Sequences and Series
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- Limits and an Introduction to Calculus
Calculus Solutions
Below are examples of Calculus math problems that can be solved.
- Evaluating Limits
- Derivatives
- Applications of Differentiation
- Applications of Integration
- Techniques of Integration
- Parametric Equations and Polar Coordinates
- Differential Equations
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Below are examples of Statistics problems that can be solved.
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- Polynomials and Expressions
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Linear Algebra Solutions
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Geometry Graphing Solutions
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- Step By Step Graphing
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2nd Grade Math Word Problems Worksheets
Math word problem worksheets for grade 2.
These word problem worksheets place 2nd grade math concepts in contexts that grade 2 students can relate to. We provide math word problems for addition, subtraction, multiplication, time, money and fractions.
We encourage students to read and think about the problems carefully, and not just recognize an answer pattern. We facilitate this by:
- providing a number of mixed word problem worksheets (e.g. subtraction questions mixed in with addition questions)
- sometimes including irrelevant data within word problems so students must understand the context before applying a solution
Addition word problems for grade 2
Simple addition (1-2 digits)
Slightly harder addition (1-3 digits)
Subtraction word problems for grade 2
Simple subtraction (1 and 2 digit numbers)
Subtracting 1-3 digit numbers
Mixed addition and subtraction word problems
Mixed addition and subtraction within 20
Mixed addition and subtraction (two digits)
More mixed addition and subtraction word problems
Multiplication word problems
Multiplication within 25
Measurement word problems
Length word problems
Time word problems
Time and elapsed time (1/2 hour intervals)
Time and elapsed time (5 minute intervals)
Money word problems
Counting money (coins and bills)
Fraction word problems
Understanding fractions
Write and compare fractions from a story
Mixed word problems
Mix of all above types of grade 2 word problems
Mix of just addition / subtraction / multiplication word problems
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18 Word Problems For Year 5: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics
Emma Johnson
Word problems for Year 5 are a great way to assess pupils’ number fluency. By the time primary school children reach Upper Key Stage 2, they will be building on their knowledge and understanding of the number system and place value, working with larger integers. An increased understanding of the connections between the different maths concepts is crucial, as children will be expected to tackle more complex, multi-step problems.
It is important children are regularly provided with the opportunity to solve a range of word problems and Year 5 maths worksheets with reasoning and problem solving incorporated alongside fluency, into all lessons.
To help you with this, we have put together a collection of 18 word problems aimed at Year 5 maths pupils.
Place value
Addition and subtraction , multiplication and division , fractions, decimals and percentages, measurement , why are word problems important in year 5 maths, how to teach problem solving in year 5, addition word problems for year 5, subtraction word problems for year 5, multiplication word problems for year 5, division word problems for year 5, fraction and decimal word problems in year 5, mixed four operation word problems, word problem resources.
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All Kinds of Word Problems
Download this free pack of multiplication word problems to help your Year 5 class grow their problem solving skills
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Year 5 maths word problems in the national curriculum
The National Curriculum states that by Year 5, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. Children also begin to use the language of algebra for solving a range of problems.
By Year 5, pupils should be starting to gain confidence in solving more complex two-step and multi-step word problems, covering topics across the Year 5 curriculum.
Solve number and practical problems involving ordering and comparing numbers to at least 1,00,000; counting forwards or backwards in steps of powers of 10; interpreting negative numbers in context and rounding to the nearest 10,100, 1000, 10,000 and 100,000.
Solve addition and subtraction word problems and a combination of these, including understanding the meaning of the equals sign.
Solve problems involving multiplication and division, including using knowledge of factors, multiples, squares and cubes and scaling by simple fractions.
Solve problems involving numbers up to 3 decimal places and problems which require knowing percentage and decimal equivalents.
Solve time word problems and those involving converting between units of time and problems involving measure (for example, length, mass, volume and money word problems ) using decimal notation and scaling.
Solve comparison, sum and difference problems, using information presented in a line graph.
Word problems are an important element of the Year 5 curriculum. By this stage, children need to be building confidence in approaching a range of one, two and multi-step word problems . They require children to be creative and apply the skills they have learnt to a range of real-life situations.
Children need to be taught the skills for successfully approaching and tackling word problems. Reading the question carefully and identifying the key information needed to tackle the problem, is the first step, followed by identifying which calculations are required for solving it and deciding whether it will be helpful to draw a picture/ visual representation to understand and answer the question.
Using mental maths skills to round and estimate an answer is also very helpful for children to establish whether their final answer is realistic. Children need to also be able to calculate the inverse, to be able to check their answer, once the problem has been completed.
See also: Mental maths year 5
Here is an example:
A transport museum has 1243 visitors on Monday morning and another 1387 visitors in the afternoon. On Tuesday 736 fewer visitors go to the museum than who visited on Monday.
How many visitors were there altogether on Tuesday?
How to solve:
What do you already know?
- The number of visitors on Monday morning and Monday afternoon are given separately. They need to be added together to give the total number of visitors for Monday.
- ‘Fewer’ means I will need to subtract the number of fewer visitors on Tuesday from the total number of visitors on Monday.
- Column addition and subtraction will be needed to solve this question.
How can this be drawn/represented pictorially?
We can draw a bar model to represent this problem:
![maths problem solving word questions year 5 problem solving](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-1.jpg)
- To calculate the total number of visitors on Monday, we need to add 1243 and 1387 together. 1243 + 1387 = 2630
- The number of fewer visitors on Tuesday needs to be subtracted from Monday’s total: 2630 – 736 = 1894.
- The total number of visitors on Tuesday was 1894.
In Year 5, addition word problems can involve whole numbers with over 4 digits and decimal numbers. Children should be able to round number to check the accuracy and begin to solve two step number problems
Addition question 1
Gemma picks two cards from the cards below and adds them together. She is able to make three different totals. What will they be?
2365 6281 9782
Answer (2 marks) : 12,147 16,063 8646
![maths problem solving word questions long addition example](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-2.jpg)
Addition question 2
Ahmed adds two of these numbers mentally.
357 280 294 232
In his calculation, he exchanges twice to create one ten and one hundred. Write Ahmed’s calculation and work out the total.
Answer (1 mark) : 357 + 294 = 651
![maths problem solving word questions long addition example](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-3.jpg)
Addition question 3
Change one digit in the calculation below, so that the answer is a multiple of 10.
Answer (1 mark) : 723 + 347 = 1070
Subtraction word problems in Year 5 require pupils to be confident subtracting numbers over 4 digits and problems involving decimal numbers. Pupils need to be able to round numbers to check accuracy and to use subtraction when solving mixed word problems.
Subtraction question 1
A coach is travelling 4924 km across the USA It has 2476 km to go. How many kilometres has the coach already travelled?
Answer (1 mark) : 2448 km
![maths problem solving word questions long subtraction example](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-4.jpg)
Subtraction question 2
A primary school printed 7283 maths worksheets in the Summer term. 2156 were for Key Stage 1 pupils. How many were printed for Key Stage 2?
Answer (1 mark): 5127 worksheets
![maths problem solving word questions long subtraction example](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-5.jpg)
Subtraction question 3
A clothing company made £57,605 profit in 2021 and £73,403 in 2022. How much more profit did the company make in 2022 than in 2021?
Answer (1 mark): £15,798
![maths problem solving word questions long subtraction example](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-6.jpg)
In year 5, multiplication word problems include problems involving times tables and multiplying whole numbers up to 4-digits by 1 or 2-digit numbers. Pupils also need to be able to combine multiplication with other operations, in order to solve two-step word problems.
Multiplication question 1
In this diagram, the numbers in the circles are multiplied together to make the answer in the square between them.
Complete the missing numbers.
![maths problem solving word questions complete the missing number](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-7.jpg)
Answer (1 mark)
![maths problem solving word questions complete the missing number answer](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-8.jpg)
Multiplication question 2
Mrs Jones was printing the end of year maths test. Each test had 18 pages and 89 pupils were sitting the test. Mrs Jones also needed to print out 12 copies for the teachers and Teaching Assistants who were helping to run the test.
How many pieces of paper did Mrs Jones need to put in the photocopier, to make sure she had enough for all the tests?
![maths problem solving word questions long multiplication](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-9.jpg)
Multiplication question 3
A school is booking a trip to Alton Towers. Tickets cost £22 per pupil. There are 120 children in each year group and all the children from 3 year groups will be going.
What will be the total price for all the tickets?
Answer (2 marks): £7920
![maths problem solving word questions long multiplication question](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-10.jpg)
Third Space Learning often ties word problems into our online one-to-one tutoring. Each lesson is personalised to the needs of the individual student, growing maths knowledge and problem solving skills.
![maths problem solving word questions multiplication word problem slide](https://thirdspacelearning.com/wp-content/uploads/2023/01/word-problems-1024x768.jpg)
In Year 5, division word problems can involve whole numbers up to 4 digits being divided by 1-digit numbers. Pupils need to understand how to answer word problems, when the answer involves a remainder.
Division question 1
Tom has 96 cubes and makes 12 equal towers. Masie has 63 cubes and makes 9 equal towers. Whose towers are tallest and by how many cubes?
Answer (2 marks): Tom
Tom’s tower has more cubes. His towers have 1 more cube than Maise’s towers.
96 ÷ 12 = 8
Division question 2
A cake factory has made cakes to deliver to a large event. 265 cakes have been baked. How many boxes of 8 cakes can be delivered to the event?
Answer (2 marks) : 33 boxes
![maths problem solving word questions long division question](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-11.jpg)
Division question 3
Lily collected 1256 stickers. She shared them between her 8 friends. How many stickers did each friend get
Answer (1 mark): 157 stickers
![maths problem solving word questions long division answer](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-12.jpg)
In Year 5, fractions word problems and decimals can include questions involving ordering, addition and subtraction of fractions. They can also involve converting between fractions and decimals.
Fraction and decimal question 1
Isobel collected 24 conkers. She gave \frac{1}{8} of the conkers to her brother. How many conkers did she have left?
Answer (1 mark): 21 conkers left
\frac{1}{8} of 24 = 3
24 – 4 = 21
Fraction and decimal question 2
Ahmed counted out 32 sweets. He gave \frac{1}{4} of the sweets to his brother and \frac{3}{8} of the sweets to his friend. How many sweets did he have left?
Answer (2 marks): 12 sweets
\frac{1}{4} of 32 = 8
\frac{3}{8} of 32 = 12
He gave away 20 sweets, so had 12 left for himself.
Fraction and decimal question 3
Two friends shared some pizzas, 1 ate 1 \frac{1}{2} pizzas, whilst the other ate \frac{5}{8} of a pizza. How much did they eat altogether?
Answer (1 mark): 2 \frac{1}{8} of pizza
1 \frac{1}{2} = \frac{12}{8}
\frac {12}{8} + \frac{5}{8} = \frac{17}{8} = 2 \frac{1}{8} pizzas
Problems with mixed operations, or ‘multi-step’ word problems, require two or more operations to solve them. A range of concepts can be covered within mixed problems, including the four operations, fractions, decimals and measures. These are worth more marks than some of the more straightforward, one-step problems.
Mixed operation question 1
At the cake sale, Sam buys 6 cookies and a cupcake . He pays £2.85 altogether. Naya buys 2 cookies and pays 90p altogether.
How much does the cupcake cost?
Answer (2 marks): 60p for one cupcake
![maths problem solving word questions money word problem](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-13.jpg)
Mixed operation question 2
Large biscuit tin – 48 biscuits (picture of boxes here) Small biscuit tin – 30 biscuits Ben bought 2 large tins of biscuits and 3 small tins.
How many biscuits did he buy altogether?
Answer (2 marks): 186 biscuits
2 x 48 = 96
3 x 30 = 90
96 + 90 = 186 biscuits
Mixed operation question 3
The owner of a bookshop bought a box of 15 books for £150.
He sold the books individually for £12 each.
How much profit did he make?
Answer (2 marks)
![maths problem solving word questions long multiplication money question](https://thirdspacelearning.com/wp-content/uploads/2023/01/Word-problems-for-year-5-blog-image-14.jpg)
Third Space Learning offers a wide array of maths and word problems resources for other year groups such as word problems for year 6 , word problems for year 3 and word problems for year 4 . Our word problem collection covers all four operations and other specific maths topics such as ratio word problems and percentage word problems .
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Praxis Core Math
Course: praxis core math > unit 1.
- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example
Algebraic word problems | Lesson
- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example
What are algebraic word problems?
What skills are needed.
- Translating sentences to equations
- Solving linear equations with one variable
- Evaluating algebraic expressions
- Solving problems using Venn diagrams
How do we solve algebraic word problems?
- Define a variable.
- Write an equation using the variable.
- Solve the equation.
- If the variable is not the answer to the word problem, use the variable to calculate the answer.
What's a Venn diagram?
- 7 + 10 − 13 = 4 brought both food and drinks.
- 7 − 4 = 3 brought only food.
- 10 − 4 = 6 brought only drinks.
- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi
- (Choice A) $ 4 A $ 4
- (Choice B) $ 5 B $ 5
- (Choice C) $ 9 C $ 9
- (Choice D) $ 14 D $ 14
- (Choice E) $ 20 E $ 20
- (Choice A) 10 A 10
- (Choice B) 12 B 12
- (Choice C) 24 C 24
- (Choice D) 30 D 30
- (Choice E) 32 E 32
- (Choice A) 4 A 4
- (Choice B) 10 B 10
- (Choice C) 14 C 14
- (Choice D) 18 D 18
- (Choice E) 22 E 22
Things to remember
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Choose Your Test
Sat / act prep online guides and tips, the complete guide to sat math word problems.
![maths problem solving word questions feature_words-1](https://blog.prepscholar.com/hs-fs/hubfs/feature_words-1.jpg?width=498&name=feature_words-1.jpg)
About 25% of your total SAT Math section will be word problems, meaning you will have to create your own visuals and equations to solve for your answers. Though the actual math topics can vary, SAT word problems share a few commonalities, and we’re here to walk you through how to best solve them.
This post will be your complete guide to SAT Math word problems. We'll cover how to translate word problems into equations and diagrams, the different types of math word problems you’ll see on the test, and how to go about solving your word problems on test day.
Feature Image: Antonio Litterio /Wikimedia
What Are SAT Math Word Problems?
A word problem is any math problem based mostly or entirely on a written description. You will not be provided with an equation, diagram, or graph on a word problem and must instead use your reading skills to translate the words of the question into a workable math problem. Once you do this, you can then solve it.
You will be given word problems on the SAT Math section for a variety of reasons. For one, word problems test your reading comprehension and your ability to visualize information.
Secondly, these types of questions allow test makers to ask questions that'd be impossible to ask with just a diagram or an equation. For instance, if a math question asks you to fit as many small objects into a larger one as is possible, it'd be difficult to demonstrate and ask this with only a diagram.
Translating Math Word Problems Into Equations or Drawings
In order to translate your SAT word problems into actionable math equations you can solve, you’ll need to understand and know how to utilize some key math terms. Whenever you see these words, you can translate them into the proper mathematical action.
For instance, the word "sum" means the value when two or more items are added together. So if you need to find the sum of a and b , you’ll need to set up your equation like this: a+b.
Also, note that many mathematical actions have more than one term attached, which can be used interchangeably.
Here is a chart with all the key terms and symbols you should know for SAT Math word problems:
Now, let's look at these math terms in action using a few official examples:
![maths problem solving word questions body_sat_math_sample_question_1](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_1.png?width=499&name=body_sat_math_sample_question_1.png)
We can solve this problem by translating the information we're given into algebra. We know the individual price of each salad and drink, and the total revenue made from selling 209 salads and drinks combined. So let's write this out in algebraic form.
We'll say that the number of salads sold = S , and the number of drinks sold = D . The problem tells us that 209 salads and drinks have been sold, which we can think of as this:
S + D = 209
Finally, we've been told that a certain number of S and D have been sold and have brought in a total revenue of 836 dollars and 50 cents. We don't know the exact numbers of S and D , but we do know how much each unit costs. Therefore, we can write this equation:
6.50 S + 2 D = 836.5
We now have two equations with the same variables ( S and D ). Since we want to know how many salads were sold, we'll need to solve for D so that we can use this information to solve for S . The first equation tells us what S and D equal when added together, but we can rearrange this to tell us what just D equals in terms of S :
Now, just subtract S from both sides to get what D equals:
D = 209 − S
Finally, plug this expression in for D into our other equation, and then solve for S :
6.50 S + 2(209 − S ) = 836.5
6.50 S + 418 − 2 S = 836.5
6.50 S − 2 S = 418.5
4.5 S = 418.5
The correct answer choice is (B) 93.
![maths problem solving word questions body_sat_math_sample_question_2](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_2.png?width=587&name=body_sat_math_sample_question_2.png)
This word problem asks us to solve for one possible solution (it asks for "a possible amount"), so we know right away that there will be multiple correct answers.
Wyatt can husk at least 12 dozen ears of corn and at most 18 dozen ears of corn per hour. If he husks 72 dozen at a rate of 12 dozen an hour, this is equal to 72 / 12 = 6 hours. You could therefore write 6 as your final answer.
If Wyatt husks 72 dozen at a rate of 18 dozen an hour (the highest rate possible he can do), this comes out to 72 / 18 = 4 hours. You could write 4 as your final answer.
Since the minimum time it takes Wyatt is 4 hours and the maximum time is 6 hours, any number from 4 to 6 would be correct.
![maths problem solving word questions body_Latin](https://blog.prepscholar.com/hs-fs/hubfs/body_Latin.jpg?width=513&name=body_Latin.jpg)
Though the hardest SAT word problems might look like Latin to you right now, practice and study will soon have you translating them into workable questions.
Typical SAT Word Problems
Word problems on the SAT can be grouped into three major categories:
- Word problems for which you must simply set up an equation
- Word problems for which you must solve for a specific value
- Word problems for which you must define the meaning of a value or variable
Below, we look at each world problem type and give you examples.
Word Problem Type 1: Setting Up an Equation
This is a fairly uncommon type of SAT word problem, but you’ll generally see it at least once on the Math section. You'll also most likely see it first on the section.
For these problems, you must use the information you’re given and then set up the equation. No need to solve for the missing variable—this is as far as you need to go.
Almost always, you’ll see this type of question in the first four questions on the SAT Math section, meaning that the College Board consider these questions easy. This is due to the fact that you only have to provide the setup and not the execution.
![maths problem solving word questions body_sat_math_sample_question_3](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_3.png?width=500&name=body_sat_math_sample_question_3.png)
To solve this problem, we'll need to know both Armand's and Tyrone's situations, so let's look at them separately:
Armand: Armand sent m text messages each hour for 5 hours, so we can write this as 5m —the number of texts he sent per hour multiplied by the total number of hours he texted.
Tyrone: Tyrone sent p text messages each hour for 4 hours, so we can write this as 4 p —the number of texts he sent per hour multiplied by the total number of hours he texted.
We now know that Armand's situation can be written algebraically as 5m , and Tyrone's can be written as 4 p . Since we're being asked for the expression that represents the total number of texts sent by Armand and Tyrone, we must add together the two expressions:
The correct answer is choice (C) 5m + 4 p
Word Problem Type 2: Solving for a Missing Value
The vast majority of SAT Math word problem questions will fall into this category. For these questions, you must both set up your equation and solve for a specific piece of information.
Most (though not all) word problem questions of this type will be scenarios or stories covering all sorts of SAT Math topics , such as averages , single-variable equations , and ratios . You almost always must have a solid understanding of the math topic in question in order to solve the word problem on the topic.
![maths problem solving word questions body_sat_math_sample_question_4](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_4.png?width=501&name=body_sat_math_sample_question_4.png)
Let's try to think about this problem in terms of x . If Type A trees produced 20% more pears than Type B did, we can write this as an expression:
x + 0.2 x = 1.2 x = # of pears produced by Type A
In this equation, x is the number of pears produced by Type B trees. If we add 20% of x (0.2 x ) to x , we get the number of pears produced by Type A trees.
The problem tells us that Type A trees produced a total of 144 pears. Since we know that 1.2 x is equal to the number of pears produced by Type A, we can write the following equation:
1.2 x = 144
Now, all we have to do is divide both sides by 1.2 to find the number of pears produced by Type B trees:
x = 144 / 1.2
The correct answer choice is (B) 120.
You might also get a geometry problem as a word problem, which might or might not be set up with a scenario, too. Geometry questions will be presented as word problems typically because the test makers felt the problem would be too easy to solve had you been given a diagram, or because the problem would be impossible to show with a diagram. (Note that geometry makes up a very small percentage of SAT Math . )
![maths problem solving word questions body_SAT_word_problem_5](https://blog.prepscholar.com/hs-fs/hubfs/body_SAT_word_problem_5.png?width=467&name=body_SAT_word_problem_5.png)
This is a case of a problem that is difficult to show visually, since x is not a set degree value but rather a value greater than 55; thus, it must be presented as a word problem.
Since we know that x must be an integer degree value greater than 55, let us assign it a value. In this case, let us call x 56°. (Why 56? There are other values x could be, but 56 is guaranteed to work since it's the smallest integer larger than 55. Basically, it's a safe bet!)
Now, because x = 56, the next angle in the triangle—2 x —must measure the following:
Let's make a rough (not to scale) sketch of what we know so far:
![maths problem solving word questions body_triangle_ex_1](https://blog.prepscholar.com/hs-fs/hubfs/body_triangle_ex_1.png?width=427&name=body_triangle_ex_1.png)
Now, we know that there are 180° in a triangle , so we can find the value of y by saying this:
y = 180 − 112 − 56
One possible value for y is 12. (Other possible values are 3, 6, and 9. )
Word Problem Type 3: Explaining the Meaning of a Variable or Value
This type of problem will show up at least once. It asks you to define part of an equation provided by the word problem—generally the meaning of a specific variable or number.
![maths problem solving word questions body_sat_math_sample_question_6](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_6.png?width=450&name=body_sat_math_sample_question_6.png)
This question might sound tricky at first, but it's actually quite simple.
We know tha t P is the number of phones Kathy has left to fix, and d is the number of days she has worked in a week. If she's worked 0 days (i.e., if we plug 0 into the equation), here's what we get:
P = 108 − 23(0)
This means that, without working any days of the week, Kathy has 108 phones to repair. The correct answer choice, therefore, is (B) Kathy starts each week with 108 phones to fix.
![maths problem solving word questions body_juggle](https://blog.prepscholar.com/hs-fs/hubfs/body_juggle.jpg?width=413&name=body_juggle.jpg)
To help juggle all the various SAT word problems, let's look at the math strategies and tips at our disposal.
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SAT Math Strategies for Word Problems
Though you’ll see word problems on the SAT Math section on a variety of math topics, there are still a few techniques you can apply to solve word problems as a whole.
#1: Draw It Out
Whether your problem is a geometry problem or an algebra problem, sometimes making a quick sketch of the scene can help you understand what exactly you're working with. For instance, let's look at how a picture can help you solve a word problem about a circle (specifically, a pizza):
![maths problem solving word questions body_sat_math_sample_question_7_2](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_7_2.png?width=450&name=body_sat_math_sample_question_7_2.png)
If you often have trouble visualizing problems such as these, draw it out. We know that we're dealing with a circle since our focus is a pizza. We also know that the pizza weighs 3 pounds.
Because we'll need to solve the weight of each slice in ounces, let's first convert the total weight of our pizza from pounds into ounces. We're given the conversion (1 pound = 16 ounces), so all we have to do is multiply our 3-pound pizza by 16 to get our answer:
3 * 16 = 48 ounces (for whole pizza)
Now, let's draw a picture. First, the pizza is divided in half (not drawn to scale):
![maths problem solving word questions body_sat_math_sample_question_7_diagram_1](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_7_diagram_1.png?width=211&name=body_sat_math_sample_question_7_diagram_1.png)
We now have two equal-sized pieces. Let's continue drawing. The problem then says that we divide each half into three equal pieces (again, not drawn to scale):
![maths problem solving word questions body_sat_math_sample_question_7_diagram_2](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_sample_question_7_diagram_2.png?width=211&name=body_sat_math_sample_question_7_diagram_2.png)
This gives us a total of six equal-sized pieces. Since we know the total weight of the pizza is 48 ounces, all we have to do is divide by 6 (the number of pieces) to get the weight (in ounces) per piece of pizza:
48 / 6 = 8 ounces per piece
The correct answer choice is (C) 8.
As for geometry problems, remember that you might get a geometry word problem written as a word problem. In this case, make your own drawing of the scene. Even a rough sketch can help you visualize the math problem and keep all your information in order.
#2: Memorize Key Terms
If you’re not used to translating English words and descriptions into mathematical equations, then SAT word problems might be difficult to wrap your head around at first. Look at the chart we gave you above so you can learn how to translate keywords into their math equivalents. This way, you can understand exactly what a problem is asking you to find and how you’re supposed to find it.
There are free SAT Math questions available online , so memorize your terms and then practice on realistic SAT word problems to make sure you’ve got your definitions down and can apply them to the actual test.
#3: Underline and/or Write Out Important Information
The key to solving a word problem is to bring together all the key pieces of given information and put them in the right places. Make sure you write out all these givens on the diagram you’ve drawn (if the problem calls for a diagram) so that all your moving pieces are in order.
One of the best ways to keep all your pieces straight is to underline your key information in the problem, and then write them out yourself before you set up your equation. So take a moment to perform this step before you zero in on solving the question.
#4: Pay Close Attention to What's Being Asked
It can be infuriating to find yourself solving for the wrong variable or writing in your given values in the wrong places. And yet this is entirely too easy to do when working with math word problems.
Make sure you pay strict attention to exactly what you’re meant to be solving for and exactly what pieces of information go where. Are you looking for the area or the perimeter? The value of x, 2x, or y?
It’s always better to double-check what you’re supposed to find before you start than to realize two minutes down the line that you have to begin solving the problem all over again.
#5: Brush Up on Any Specific Math Topic You Feel Weak In
You're likely to see both a diagram/equation problem and a word problem for almost every SAT Math topic on the test. This is why there are so many different types of word problems and why you’ll need to know the ins and outs of every SAT Math topic in order to be able to solve a word problem about it.
For example, if you don’t know how to find an average given a set of numbers, you certainly won’t know how to solve a word problem that deals with averages!
Understand that solving an SAT Math word problem is a two-step process: it requires you to both understand how word problems work and to understand the math topic in question. If you have any areas of mathematical weakness, now's a good time to brush up on them—or else SAT word problems might be trickier than you were expecting!
![maths problem solving word questions body_ready-1](https://blog.prepscholar.com/hs-fs/hubfs/body_ready-1.png?width=353&name=body_ready-1.png)
All set? Let's go!
Test Your SAT Math Word Problem Knowledge
Finally, it's time to test your word problem know-how against real SAT Math problems:
Word Problems
1. No Calculator
![maths problem solving word questions body_sat_math_test_question_1](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_test_question_1.png?width=400&name=body_sat_math_test_question_1.png)
2. Calculator OK
![maths problem solving word questions body_sat_math_test_question_2](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_test_question_2.png?width=400&name=body_sat_math_test_question_2.png)
3. Calculator OK
![maths problem solving word questions body_sat_math_test_question_3](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_test_question_3.png?width=400&name=body_sat_math_test_question_3.png)
4. Calculator OK
![maths problem solving word questions body_sat_math_test_question_4](https://blog.prepscholar.com/hs-fs/hubfs/body_sat_math_test_question_4.png?width=400&name=body_sat_math_test_question_4.png)
Answers: C, B, A, 1160
Answer Explanations
1. For this problem, we have to use the information we're given to set up an equation.
We know that Ken spent x dollars, and Paul spent 1 dollar more than Ken did. Therefore, we can write the following equation for Paul:
Ken and Paul split the bill evenly. This means that we'll have to solve for the total amount of both their sandwiches and then divide it by 2. Since Ken's sandwich cost x dollars and Paul's cost x + 1, here's what our equation looks like when we combine the two expressions:
Now, we can divide this expression by 2 to get the price each person paid:
(2 x + 1) / 2
But we're not finished yet. We know that both Ken and Paul also paid a 20% tip on their bills. As a result, we have to multiply the total cost of one bill by 0.2, and then add this tip to the bill. Algebraically, this looks like this:
( x + 0.5) + 0.2( x + 0.5)
x + 0.5 + 0.2 x + 0.1
1.2 x + 0.6
The correct answer choice is (C) 1.2 x + 0.6
2. You'll have to be familiar with statistics in order to understand what this question is asking.
Since Nick surveyed a random sample of his freshman class, we can say that this sample will accurately reflect the opinion (and thus the same percentages) as the entire freshman class.
Of the 90 freshmen sampled, 25.6% said that they wanted the Fall Festival held in October. All we have to do now is find this percentage of the entire freshmen class (which consists of 225 students) to determine how many total freshmen would prefer an October festival:
225 * 0.256 = 57.6
Since the question is asking "about how many students"—and since we obviously can't have a fraction of a person!—we'll have to round this number to the nearest answer choice available, which is 60, or answer choice (B).
3. This is one of those problems that is asking you to define a value in the equation given. It might look confusing, but don't be scared—it's actually not as difficult as it appears!
First off, we know that t represents the number of seconds passed after an object is launched upward. But what if no time has passed yet? This would mean that t = 0. Here's what happens to the equation when we plug in 0 for t :
h (0) = -16(0)2 + 110(0) + 72
h (0) = 0 + 0 + 72
As we can see, before the object is even launched, it has a height of 72 feet. This means that 72 must represent the initial height, in feet, of the object, or answer choice (A).
4. You might be tempted to draw a diagram for this problem since it's talking about a pool (rectangle), but it's actually quicker to just look at the numbers given and work from there.
We know that the pool currently holds 600 gallons of water and that water has been hosed into it at a rate of 8 gallons a minute for a total of 70 minutes.
To find the amount of water in the pool now, we'll have to first solve for the amount of water added to the pool by hose. We know that 8 gallons were added each minute for 70 minutes, so all we have to do is multiply 8 by 70:
8 * 70 = 560 gallons
This tells us that 560 gallons of water were added to our already-filled, 600-gallon pool. To find the total amount of water, then, we simply add these two numbers together:
560 + 600 = 1160
The correct answer is 1160.
![maths problem solving word questions body_sleepy-1](https://blog.prepscholar.com/hs-fs/hubfs/body_sleepy-1.jpg?width=463&name=body_sleepy-1.jpg)
Aaaaaaaaaaand time for a nap.
Key Takeaways: Making Sense of SAT Math Word Problems
Word problems make up a significant portion of the SAT Math section, so it’s a good idea to understand how they work and how to translate the words on the page into a proper expression or equation. But this is still only half the battle.
Though you won’t know how to solve a word problem if you don’t know what a product is or how to draw a right triangle, you also won’t know how to solve a word problem about ratios if you don’t know how ratios work.
Therefore, be sure to learn not only how to approach math word problems as a whole, but also how to narrow your focus on any SAT Math topics you need help with. You can find links to all of our SAT Math topic guides here to help you in your studies.
What’s Next?
Want to brush up on SAT Math topics? Check out our individual math guides to get an overview of each and every topic on SAT Math . From polygons and slopes to probabilities and sequences , we've got you covered!
Running out of time on the SAT Math section? We have the know-how to help you beat the clock and maximize your score .
Been procrastinating on your SAT studying? Learn how you can overcome your desire to procrastinate and make a well-balanced prep plan.
Trying to get a perfect SAT score? Take a look at our guide to getting a perfect 800 on SAT Math , written by a perfect scorer.
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Grade 9 Algebra Word Problems
Related Pages Grade 8 Algebra Word Problems Algebra Word Problems Solving Equations More Algebra Lessons
These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions. It includes various examples and solutions for algebra word problems that you will commonly encounter in 9th grade.
Age Word Problems
Age Problems with two unknowns or variables
Example: Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?
Solution: Let x represent Spenser’s age Therefore, Taylor’s age is 5x x + 5x = 18 6x = 18 x = 3 Therefore, Spenser is 3 years old and Taylor is 15 years old.
Grade 9 Algebra Word Problems - Age
Example 1: A mother is three times as old as her daughter. Six years ago, the mother’s age was six tines that of her daughter. How old are they now?
Solution: Let x represent the daughter’s age. Therefore, 3x is the mother’s age. 6(x - 6) = 3x - 6 6x - 6 = 3x - 6 3x = 30 x = 10 Therefore, the daughter’s is 10 years old and the mother is 30 years old.
Example 2: A father is now three times as old as his son. Eight years ago, the father was five times as old as his son. How old are they now?
Rate, Distance, Time Word Problems
Grade 9 Algebra Word Problems - Rate, Distance, Time
Example: A bus leaves the terminal and averages 40 km/hr. One hour late, a second bus leaves the same terminal and averages 50 km/hr. In how many hours will the second bus overtake the first?
Grade 9 Rate, Distance, Time Word Problems
Example 1: One motorist travels 5 km.hr faster than another. They leave from the same place and travel in opposite directions. What is the rate of each if they are 195 km apart after 3 hours?
Example 2: A pilot flew from airport A to airport B at a rate of 100 km/hr and flew back from airport B to airport A at 120 km/hr. The total time it took was 11 hours. How far is it from airport A to airport B?
Coin Word Problems
Grade 9 Algebra Word Problems - Coins
Example: A coin collection amounting to $25 consists of nickels and dimes. There are 3 times as many nickels and dimes. There are 3 times as many nickels as dimes. How many coins of each kind are there?
Solution: Let x = number of dimes 3x = number of nickels 10x + 5(3x) = 2500 25x = 2500 x = 100 Therefore, there are 100 dimes and 300 nickels.
Grade 9 Coin Algebra Word Problems
Example: Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of each kind does he have?
Coin Algebra Word Problems - Grade 9
Example: Bob has in his pocket a number of pennies, 5 times as many nickels as pennies and 5 more quarters than pennies. The coins amount to $2.27. Find the number of each kind of coin.
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On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a ...
An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.
Math Word Problem Worksheets. Read, explore, and solve over 1000 math word problems based on addition, subtraction, multiplication, division, fraction, decimal, ratio and more. These word problems help children hone their reading and analytical skills; understand the real-life application of math operations and other math topics.
Year 3 are collecting pebbles. This pictogram shows the different numbers of pebbles each group finds. Answer: a) 9 b) 3 pebbles drawn. Top tip. By the time children are in Year 3 many of the word problems, even one-step story problems tend to be a variation on a multiplication problem.
Math word problem worksheets for grade 5. These worksheets present students with real world word problems that students can solve with grade 5 math concepts.. We encourage students to think about the problems carefully by: providing a number of mixed word problem worksheets; including irrelevant data so students need to understand the context before applying a solution
Grade 3 word problems worksheets. Simple addition word problems (numbers under 100) Addition in columns (numbers under 1,000) Mental subtraction. Subtraction in columns (2-3 digits) Mixed addition and subtraction. Simple multiplication (1-digit by 1 or 2-digit) Multiplying multiples of 10. Multiplication in columns.
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Math Word Problems worksheets are an essential tool for teachers to help their students develop strong problem-solving skills and a deep understanding of mathematical concepts. These worksheets cover a wide range of topics, from basic arithmetic to advanced algebra, and are designed to challenge students at every grade level. ...
Click to see solution. Problem 17. A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker. Click to see solution. Problem 18.
Math Word Problem Solutions. Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms. Word ...
These word problem worksheets place 2nd grade math concepts in contexts that grade 2 students can relate to. We provide math word problems for addition, subtraction, multiplication, time, money and fractions. We encourage students to read and think about the problems carefully, and not just recognize an answer pattern. We facilitate this by:
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The vast majority of SAT Math word problem questions will fall into this category. For these questions, ... Understand that solving an SAT Math word problem is a two-step process: it requires you to both understand how word problems work and to understand the math topic in question. If you have any areas of mathematical weakness, now's a good ...
Grade 9 Algebra Word Problems - Age. Example 1: A mother is three times as old as her daughter. Six years ago, the mother's age was six tines that of her daughter. How old are they now? Solution: Let x represent the daughter's age. Therefore, 3x is the mother's age. 6 (x - 6) = 3x - 6.
How many does she have? Add the values 3, 4 and 0.5. Integrate x^2 (x+1) Find the derivative of sin (2x + 1) Alex has two books. Chris has nine books. If Chris gives every book he has to Alex, how many books will Alex have? Solve x^2-5x+6=0 using the quadratic formula. Find the differential dy of y=cos (x)
Age word problems typically involve comparing two people's ages at different points in time, i.e. at present, in the past, or in the future. This lesson is divided into two parts. Part I involves age word problems that can be solved using a single variable while Part II contains age word problems that need to be solved using two variables .
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