lesson 4 problem solving practice add and subtract unlike fractions answers

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As you can see, the least common denominator lets you add (or subtract) fractions using the least number of slices. It is not always practical to draw circles to solve these problems. So we need an arithmetic method. We will use  equivalent fractions  to help us, as shown in the examples below.

Example 1: 

The denominators are not the same.  The least common denominator (LCD) of 4 and 6  is 12.

Solution:  Make equivalent fractions with the new denominator:

Add the numerators:

In example 1, note that the numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions. We could have used a common denominator, such as 24, to solve this problem. This is shown below.

As you can see, using a common denominator instead of the LCD can lead to unnecessary simplifying of the result (like having more slices of pizza). We have presented two methods for adding (and subtracting) fractions with unlike denominators:

• Common denominators — leads to having more slices of pizza.
• Least common denominator (LCD) — leads to having less slices of pizza.

You can use either method, whichever you prefer. However, for the remainder of this lesson, we will use the LCD method. Remember that the LCD is simply the least common multiple of the denominators. Let’s look at some examples.

Example 2: 

Anaysis:  The denominators are not the same. The  LCD of 3 and 2  is 6.

Solution:  Make equivalent fractionswith the new denominator:

Simply the result:

In example 2, we had an improper fraction, so it was necessary to simplify the result. Let’s look at some more examples.

Example 3: 

Analysis:  The denominators are not the same. The  LCD of 10 and 15  is 30.

Subtract the numerators:

Example 4: 

Analysis:  The denominators are not the same. The  LCD of 6, 8 and 16  is 48.

Subtract and add the numerators:

The following procedure summarizes the steps we used in examples 1 through 4:

Procedure:  To add or subtract fractions with unlike denominators:

• Find the least common denominator.
• Make equivalent fractions using the LCD.
• Add or subtract the numerators.
• Simplify the result if necessary.

For step 2, remember that the numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions. Let’s look at some word problems.

Analysis:  This problem is asking us to add fractions with unlike denominators:

Solution:  The LCD of 3 and 5 is 15.

Analysis:  This problem is asking us to subtract fractions with unlike denominators:

Solution:  The LCD of 4 and 2 is 4.

Summary:  In order to add or subtract fractions, they must have like denominators. Given two or more fractions with unlike denominators, the LCD is the least common multiple of the denominators.

To add or subtract fractions with unlike denominators

Directions: Add the fractions in each exercise below.  Be sure to simplify your result, if necessary.  Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

• Math Article

Addition of Fractions

The addition of fractions teaches us to add two or more fractions with the same or different denominators. The addition  of fraction depends  on two major conditions: 

• Same denominators
• Different denominators

While adding fractions, if denominators are the same (such fractions are said to be like fractions), then they can be added directly. But if the denominators are different, (such fractions are called unlike fractions) then we need to make the denominators same and then add the fractions. Learn  like or unlike fractions , here.

Addition of Fractions with Same Denominators

If denominators of two or more fractions are same, then we can directly add the numerators, keeping the denominator common. 

Follow the below steps to add the fractions with same denominators:

• Add the numerators together, keeping the denominator common
• Write the simplified fraction

For example: Add the fractions: 5/6 and 7/6.

Since the denominators are same, therefore we can add the numerators directly.

(5/6) + (7/6) = (5 + 7)/6 = 12/6

• Simplify the fraction

Hence, the sum of ⅚ and 7/6 is 2.

Adding fractions with Different Denominators

When two or more fractions with different denominators are added together, then we cannot the numerators directly. 

Follow the below steps to add fractions with different denominators:

• Check the denominators of the fractions.
• Make the denominators of the fractions same, by finding the LCM of denominators and rationalising them
• Add the numerators of the fractions, keeping the denominator common
• Simplify the fraction to get final sum

For example: Add 3/12 + 5/2

Solution: Both the fractions 3/12 and 5/2 have different denominators.

We can write 3/12 = ¼, in a simplified fraction.

Now, ¼ and 5/2 are two fractions.

LCM of 2 and 4 = 4

Multiply 5/2 by 2/2.

5/2 x 2/2 = 10/4

Now add ¼ and 10/4

¼ + 10/4 = (1+10)/4 = 11/4

Hence, the sum of 3/12 and 5/2 is 11/4.

Adding fractions with whole numbers

Add the fraction and a whole number with three simple steps:

• Write the given whole number in the form of a fraction (for example, 3/1)
• Make the denominators same and add the fractions

For example: Add 7/2 + 4

Here, 7/2 is a fraction and 4 is a whole number.

We can write 4 as 4/1.

Now making the denominators same, we get;

7/2 and 4/1 x (2/2) = 8/2

Add 7/2 and 8/2

7/2 + 8/2 = 15/2

Hence, the sum of 7/2 and 4 is 15/2.

Adding Fractions with Co-prime Denominators

Co-prime  denominators : The denominators which do not have common factors, other than 1.

Let us learn how to add fractions with co-prime denominators with the help of the following steps:

• Check the denominators whether they are co-prime
• Multiply the first fraction (numerator and denominator) with the denominator of the other fraction and the second fraction (numerator and denominator) with the denominator of the first fraction.
• Add the resulting fractions and simplify

For example, the addition of fractions 9/7 and 3/4 can be done as follows.

The denominators 7 and 4 are coprime since they have only one highest common factor 1.

So, (9/7) + (3/4) = [(9 × 4) + (3 × 7)]/ (7 × 4)

= (36 + 21)/28

Adding Mixed Fractions

A mixed fraction is a combination of a whole number and a fraction. To add two mixed fractions, we need to convert them first into improper fractions and then add them together.

Follow the below steps to add mixed numbers:

• Convert the given mixed fraction into improper fractions
• Check if denominators are the same or different
• If different denominators, then rationalise them
• Add the fractions and simplify

Let’s understand how to add mixed fractions with an example:

Example: Add : 3 ⅓  + 1 ¾

Step1: Convert the given mixed fractions to improper fractions.

3 ⅓  = 10/3 

Step 2: Make the denominators same by taking the LCM and multiplying the suitables fractions for both.

LCM of 3 and 4 is 12.

So, 10/3 = (10/3) × (4/4) = 40/12

7/4 = (7/4) × (3/3) = 21/12

Step 3: Take the denominator as common and add numerators.  Then, write the final answer.

(40/12) + (21/12) = (40 + 21)/12 = 61/12      

Therefore, 3 ⅓  + 1 ¾ = 61/12 = 5 1/12

Subtraction of Fractions

As we know, addition and subtraction are similar operations in Maths. In addition, we add two or more numbers, whereas, in subtraction, we subtract a number from another. Therefore, subtraction of fractions also follows the same rule as addition of fractions. 

If the denominators are the same for given fractions, then we can directly subtract the numerator, keeping the denominator same.

If the denominators of fractions are different, we need to rationalise them first and then perform subtraction. 

Some examples are:

Example 1: Subtract ⅓ from 8/3.

Solution: We need to find,

8/3 – ⅓ = ?

Since the denominator of two fractions ⅓ and 8/3 is common, therefore, we can directly subtract them:

8/3 – ⅓ = (8-1)/3 = 7/3

Example 2: Subtract ½ from ¾. 

Solution: We need to subtract ½ from ¾, i.e.,

¾ – ½ = ?

Since the denominators of two fractions are different, therefore, we need to rationalise them by taking the LCM.

LCM (4,2) = 4

Now multiply the ½ by 2/2, to get 2/4

¾ – 2/4 = (3-2)/4 = ¼

Hence, ¾ – ½ = ¼

Video Lesson on Fractions

Solved Examples

Let us solve some problems based on adding fractions.

Q. 1: Add 1/2 and 7/2.

Solution: Given fractions: 1/2 and 7/2 Since the denominators are the same, hence we can just add the numerators here, keeping the denominator as it is.

Q. 2: Add 3/5 and 4.

Solution: We can write 4 as 4/1

Now, 3/5 and 4/1 are the two fractions to be added.

Since the denominators here are different, thus we need to simplify the denominators first, before adding the fractions.

Taking LCM of 5 and 1, we get;

LCM(5,1) = 5

Therefore, multiplying the second fraction, 4/1 by 5 both in numerator and denominator, we get;

(4×5)/((1×5) = 20/5

Now 3/5 and 20/5 have a common denominator, i.e. 5, therefore, adding the fractions now;

Addition of Fraction Worksheet

Fraction addition is one of the important topics in classes 6, 7 and 8. We have provided a worksheet for the addition of fractions here. After practising the questions given in this worksheet, you’ll be able to solve ant fraction addition sums easily. Practice from the given addition of fraction worksheet link here and score well in exams.

Practice Questions

• 1(⅓) + 3(5/2) = 
• 2(¾) + ___ = 7
• 3/7 + 2 + 4/3 = ?

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Frequently Asked Questions – FAQs

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Fractions: Add and Subtract Unlike Denominators

In this lesson, students will learn to solve addition and subtraction problems with unlike denominators. Students will learn methods and strategies for solving these problems and will practice solving them with the worksheets.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. All of the optional adjustments for this lesson are for the activity. One of the optional additions to this lesson is to have students create their own War problems on index cards, creating various levels of difficulty.

Description

Additional information, what our fractions: add and subtract unlike denominators lesson plan includes.

Lesson Objectives and Overview: Fractions: Add and Subtract Unlike Denominators teaches students how to add or subtract fractions with unlike denominators. They will know how to add or subtract fractions with like denominators. Students practice solving problems as a part of this lesson. This lesson is for students in 5th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The only supplies you will need for this lesson are scissors. To prepare for this lesson ahead of time, you can gather the supplies and copy the handouts.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. All of the optional adjustments for this lesson are for the activity. You can have students create their own War problems on index cards, creating various levels of difficulty. Students can play in groups of three or four. If you have students who are struggling, you can make sure they only use denominators under 6. Finally, if you have students who need more of a challenge, you can either use larger numbers or incorporate three numbers into the expression to make it more difficult.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.

FRACTIONS: ADD AND SUBTRACT UNLIKE DENOMINATORS LESSON PLAN CONTENT PAGES

Fractions – add and subtract unlike denominators.

The Fractions: Add and Subtract Unlike Denominators lesson plan includes three content pages. The lesson begins by stating that you have to have a common denominator (the same denominator) to add or subtract fractions. The bottom number in a fraction is called the denominator. The lesson shows examples of common and unlike (different) denominators. In order to find a common denominator, you need to find the least common multiple.

For the example problem 2/3 + 1/9, we must first find the least common multiple of 3 and 9. Multiples of 3 are 3, 6, 9, and multiples of 9 start with 9. Therefore, the least common multiple is 9. Next, you must multiply both the numerator and the denominator by 3 in the first fraction to create the common denominator, because 3 x 3 = 9 (the new denominator). The original fraction is 2/3, so the new one is 6/9 (2 x 3 = 6 and 3 x 3 = 9). You can then add the fractions together easily. 6/9 + 1/9 = 7/9.

The lesson next shows another addition example and a subtraction example that uses the same process. It then shows an example that includes a mixed number. For mixed numbers, you must first change the mixed number into an improper fraction. You then solve using the same method! Your final answer can be written either as an improper fraction or you can change it back to a mixed number.

FRACTIONS: ADD AND SUBTRACT UNLIKE DENOMINATORS LESSON PLAN WORKSHEETS

The Fractions: Add and Subtract Unlike Denominators lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

WAR ACTIVITY WORKSHEET

For the activity worksheet, students will play a fun game of War using the provided cards (which they will need to cut out of the worksheet). To play, each student will flip over a card and solve the problem. The highest card wins!

SOLVE THE PROBLEMS PRACTICE WORKSHEET

The practice worksheet asks students to solve 12 addition or subtraction problems. They must show their work and circle their answer.

FRACTIONS: ADD AND SUBTRACT UNLIKE DENOMINATORS HOMEWORK ASSIGNMENT

For the homework assignment, which is structured in the same way as the practice worksheet, students will solve 12 addition or subtraction problems. They must show their work and circle their answer.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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Lesson Plan on Adding and Subtracting Fractions with Unlike Denominators

Lesson Title :Adding and Subtracting Fractions with Unlike Denominators

Lesson Objective : Students will be able to demonstrate understanding of adding and subtracting fractions with unlike denominators by solving problems and explaining their thinking.

Materials :

• Fraction strips
• Fraction circles
• Whiteboard and markers
• Fraction worksheet
• Fraction manipulative (optional)
• LCD (Least common denominator) chart

Introduction (5 minutes) : Begin the lesson by reviewing what a fraction is and the parts of a fraction (numerator and denominator). Explain to students that today they will be learning about adding and subtracting fractions with unlike denominators.

Direct Instruction (15 minutes): Using the whiteboard, demonstrate how to add and subtract fractions with unlike denominators. For example, show students how to add 2/3 + 1/4 and how to subtract 3/5 – 2/4. Use different visual aids such as fraction strip and circles to make the concept clear. Also, explain the concept of LCD (Least common denominator) and how it can be used to add and subtract fractions with unlike denominators.

Guided Practice (10 minutes): Have students work in pairs to solve problems on the whiteboard. Provide them with a set of problems that have unlike denominators. As they work, circulate the room to provide support and guidance as needed.

Independent Practice (20 minutes): Provide students with a worksheet that includes a variety of problems that require them to add and subtract fractions with unlike denominators. Encourage them to use fraction manipulative and LCD chart to help them visualize the problem. Have them work independently and check their answers with a partner.

Closure (5 minutes): Ask students to share their answers and have them explain their thinking. Review any misconceptions and provide additional support as needed.

Assessment : The worksheet completed during independent practice will be collected and used to assess student understanding of adding and subtracting fractions with unlike denominators.

Note : It’s important to point out that the concept of adding and subtracting with unlike denominators should be taught after students have a good understanding of the concept of fractions and equivalent fractions. It’s also important to use different visual aids and manipulatives to help students understand and visualize the concept. It’s also important to give ample practice problems with different denominators to help them master the concept. Also, it’s important to stress the importance of finding the least common denominator when adding and subtracting unlike denominators. It’s also important to give ample practice problems with different denominators to help them master the concept.

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Addition and Subtraction of Unlike Fractions – Definition, Facts, Examples | How to Add and Subtract Unlike Fractions?

Addition and Subtraction of Unlike Fractions are different compared to the addition and subtraction of the like fractions. The, unlike fractions, are fractions that have different denominators. It is a bit difficult to add or subtract, unlike fractions compared to like fractions. But if you go through this entire article, you will find the easy way to learn addition and subtraction of unlike fractions.

Different ways have been given to solve the unlike fractions with solved examples and images. Learn the addition and subtraction of Unlike Fractions by referring to the entire article. You can get all the 6th Grade Math Concepts and their worksheets on our website. Also, take the practice sessions and cross-check your answers for the best practice. We have given the best way of learning for students with our concepts.

Also, find:

• Comparing Unlike Fractions
• Like and Unlike Fractions
• Addition and Subtraction of Like Fractions

How to Add Unlike Fractions? | Adding Fractions with Unlike Denominators

The addition of unlike fractions is the process of adding fractions having different denominators. Check out the addition of unlike fractions with the following procedure.

1. Firstly, take the given fractions with their denominators. 2. Then, take the LCM of the given unlike fractions. Or you can also take the cross multiplication of fractions. 3. Convert the unlike fractions into like fractions. 4. Finally, add the like fractions and write down the final answer.

Addition of Unlike Fractions Examples

We have given different problems along with their explanation and answers. Go through the all problems and learn the complete concept clearly.

Question 1. \(\frac { 3 }{ 2 } \) + \(\frac { 3 }{ 4 } \)

Therefore, the final answer is \(\frac { 10 }{ 4 } \).

Question 2. \(\frac { 2 }{ 6 } \) + \(\frac { 6 }{ 8 } \)

Therefore, the final answer is \(\frac { 26 }{ 24 } \).

Question 3. Add 2 \(\frac { 3 }{ 4 } \) and 3 \(\frac { 2 }{ 5 } \)

Therefore, the final answer is \(\frac { 123 }{ 20 } \).

How to Subtract Unlike Fractions?

The subtraction of unlike fractions is completely different compared to subtraction of like fractions which are having different denominators. Check out the subtraction of unlike fractions with the following procedure.

1. Firstly, take the given fractions with their denominators. 2. Then, take the LCM of the given unlike fractions. Or you can also take the cross multiplication of fractions. 3. Convert the unlike fractions into like fractions. 4. Finally, Subtract the like fractions and write down the final answer.

Subtracting Unlike Fractions Examples

Question 1. Find the difference of \(\frac { 4 }{ 6 } \) and \(\frac { 3 }{ 9 } \)

Therefore, the final answer is \(\frac { 6 }{ 18 } \).

Question 2. Find the difference of \(\frac { 17 }{ 12 } \) and \(\frac { 15 }{ 8 } \)

Therefore, the final answer is \(\frac { 11 }{ 24 } \).

Question 3. Find the difference of 2 \(\frac { 3 }{ 4 } \) and 3 \(\frac { 2 }{ 5 } \)

Therefore, the final answer is \(\frac { 13 }{ 20 } \).

FAQs on Adding and Subtracting Unlike Fractions

1. What is an Unlike Fraction with Example?

An unlike fraction can defined as the fractions consisting of different denominators. That means the fractions having different number in the denominator are called as the unlike fractions. Examples of Unlike fractions are \(\frac { 1 }{ 3 } \), \(\frac { 3 }{ 6 } \), \(\frac { 4 }{ 7 } \).

2. How to Add Unlike Fractions?

To add Unlike fractions, convert the unlike fractions to like fractions. Then, just add their numerators and note down the sum as the addition of numerators over the common denominator. For example, 3/10 + 4/5 = (3 + 8)/10 = 11/10.

3. How to Subtract Unlike Fractions?

To subtract Unlike fractions, convert the unlike fractions to like fractions. Then, just subtract their numerators and note down the subtraction as the subtraction of numerators over the common denominator. For example, 5/4 – 3/8 = (10 – 3)/8 = 7/8.

4. How to covert unlike fractions into like fractions?

There are two simple ways available to convert unlike fractions into like fractions. They are the LCM method and cross multiplication method. You can choose any one of the methods to convert the unlike fractions into like fractions. Then, you can easily perform arithmetic operations like addition and subtraction, etc.

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Exploring Unlike Fractions - Lesson Plan

Join us on an exciting math adventure as we unlock the power of comparing unlike fractions. in this interactive lesson, students will learn various strategies to compare fractions with different denominators. from using one whole to finding common denominators, students will develop a deep understanding of fraction comparison. through engaging tasks and activities, students will practice their skills and apply their knowledge to real-world scenarios. by the end of this lesson, students will be confident in their ability to compare unlike fractions and make informed mathematical decisions..

Know more about Exploring Unlike Fractions - Lesson Plan

In this lesson, students will learn various strategies for comparing unlike fractions, including using one whole and finding the common denominator.

Finding a common denominator allows us to make equivalent fractions and accurately compare the numerators.

You can apply your knowledge by solving real-world problems that involve comparing quantities or measurements represented by unlike fractions.

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How to Add and Subtract Fractions and Mixed Numbers With Unlike Denominators

Finding a Common Denominator

So, What Did You Learn?

Subtracting fractions with unlike denominators.

Adding Mixed Numbers

71/12 in mixed fraction is 5 11/12 . ✅

Subtracting Mixed Numbers

65/10 - 28/10 = 37/10

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