my homework lesson 6 add mixed numbers

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Arithmetic (all content)

Course: arithmetic (all content)   >   unit 5, intro to adding mixed numbers.

• Intro to subtracting mixed numbers
• Add and subtract mixed numbers (no regrouping)
• Add and subtract mixed numbers (with regrouping)

Want to join the conversation?

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

Video transcript

• Notifications 0

• Add Friend ($5)

As a registered member you can:

• View all solutions for free
• Request more in-depth explanations for free
• Ask our tutors any math-related question for free
• Email your homework to your parent or tutor for free
• Grade 5 HMH Go Math - Answer Keys

Yes, email page to my online tutor. ( if you didn't add a tutor yet, you can add one here )

Thank you for doing your homework!

Submit Your Question

4.6 Add and Subtract Mixed Numbers

Learning objectives.

• Model addition of mixed numbers with a common denominator
• Add mixed numbers with a common denominator
• Model subtraction of mixed numbers
• Subtract mixed numbers with a common denominator
• Add and subtract mixed numbers with different denominators

Be Prepared 4.6

Before you get started, take this readiness quiz.

• Draw figure to model 7 3 . 7 3 . If you missed this problem, review Example 4.6 .
• Change 11 4 11 4 to a mixed number. If you missed this problem, review Example 4.9 .
• Change 3 1 2 3 1 2 to an improper fraction. If you missed this problem, review Example 4.11 .

Model Addition of Mixed Numbers with a Common Denominator

So far, we’ve added and subtracted proper and improper fractions, but not mixed numbers. Let’s begin by thinking about addition of mixed numbers using money.

If Ron has 1 1 dollar and 1 1 quarter, he has 1 1 4 1 1 4 dollars.

If Don has 2 2 dollars and 1 1 quarter, he has 2 1 4 2 1 4 dollars.

What if Ron and Don put their money together? They would have 3 3 dollars and 2 2 quarters. They add the dollars and add the quarters. This makes 3 2 4 3 2 4 dollars. Because two quarters is half a dollar, they would have 3 3 and a half dollars, or 3 1 2 3 1 2 dollars.

When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.

We can use fraction circles to model this same example:

Manipulative Mathematics

Example 4.81.

Model 2 1 3 + 1 2 3 2 1 3 + 1 2 3 and give the sum.

We will use fraction circles, whole circles for the whole numbers and 1 3 1 3 pieces for the fractions.

This is the same as 4 4 wholes. So, 2 1 3 + 1 2 3 = 4 . 2 1 3 + 1 2 3 = 4 .

Try It 4.161

Use a model to add the following. Draw a picture to illustrate your model.

1 2 5 + 3 3 5 1 2 5 + 3 3 5

Try It 4.162

2 1 6 + 2 5 6 2 1 6 + 2 5 6

Example 4.82

Model 1 3 5 + 2 3 5 1 3 5 + 2 3 5 and give the sum as a mixed number.

We will use fraction circles, whole circles for the whole numbers and 1 5 1 5 pieces for the fractions.

Adding the whole circles and fifth pieces, we got a sum of 3 6 5 . 3 6 5 . We can see that 6 5 6 5 is equivalent to 1 1 5 , 1 1 5 , so we add that to the 3 3 to get 4 1 5 . 4 1 5 .

Try It 4.163

Model, and give the sum as a mixed number. Draw a picture to illustrate your model.

2 5 6 + 1 5 6 2 5 6 + 1 5 6

Try It 4.164

1 5 8 + 1 7 8 1 5 8 + 1 7 8

Add Mixed Numbers

Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.

Add mixed numbers with a common denominator.

Step 1. Add the whole numbers.

Step 2. Add the fractions.

Step 3. Simplify, if possible.

Example 4.83

Add: 3 4 9 + 2 2 9 . 3 4 9 + 2 2 9 .

Try It 4.165

Find the sum: 4 4 7 + 1 2 7 . 4 4 7 + 1 2 7 .

Try It 4.166

Find the sum: 2 3 11 + 5 6 11 . 2 3 11 + 5 6 11 .

In Example 4.83 , the sum of the fractions was a proper fraction . Now we will work through an example where the sum is an improper fraction.

Example 4.84

Find the sum: 9 5 9 + 5 7 9 . 9 5 9 + 5 7 9 .

Try It 4.167

Find the sum: 8 7 8 + 7 5 8 . 8 7 8 + 7 5 8 .

Try It 4.168

Find the sum: 6 7 9 + 8 5 9 . 6 7 9 + 8 5 9 .

An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.

Example 4.85

Add by converting the mixed numbers to improper fractions: 3 7 8 + 4 3 8 . 3 7 8 + 4 3 8 .

Since the problem was given in mixed number form, we will write the sum as a mixed number.

Try It 4.169

Find the sum by converting the mixed numbers to improper fractions:

5 5 9 + 3 7 9 . 5 5 9 + 3 7 9 .

Try It 4.170

3 7 10 + 2 9 10 . 3 7 10 + 2 9 10 .

Table 4.2 compares the two methods of addition, using the expression 3 2 5 + 6 4 5 3 2 5 + 6 4 5 as an example. Which way do you prefer?

Model Subtraction of Mixed Numbers

Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.

We will use fraction circles (pizzas!) to help us visualize the process.

Start with one whole.

Algebraically, you would write:

Example 4.86

Use a model to subtract: 1 − 1 3 . 1 − 1 3 .

Try It 4.171

Use a model to subtract: 1 − 1 4 . 1 − 1 4 .

Try It 4.172

Use a model to subtract: 1 − 1 5 . 1 − 1 5 .

What if we start with more than one whole? Let’s find out.

Example 4.87

Use a model to subtract: 2 − 3 4 . 2 − 3 4 .

Try It 4.173

Use a model to subtract: 2 − 1 5 . 2 − 1 5 .

Try It 4.174

Use a model to subtract: 2 − 1 3 . 2 − 1 3 .

In the next example, we’ll subtract more than one whole.

Example 4.88

Use a model to subtract: 2 − 1 2 5 . 2 − 1 2 5 .

Try It 4.175

Use a model to subtract: 2 − 1 1 3 . 2 − 1 1 3 .

Try It 4.176

Use a model to subtract: 2 − 1 1 4 . 2 − 1 1 4 .

What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a $1 $1 bill and one quarter. What could you do? You could change the dollar bill into 4 4 quarters. The value of 4 4 quarters is the same as one dollar bill, but the 4 4 quarters are more useful for the parking meter. Now, instead of having a $1 $1 bill and one quarter, you have 5 5 quarters and can put 3 3 quarters in the meter.

This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.

We can also model this using fraction circles, much like we did for addition of mixed numbers.

Example 4.89

Use a model to subtract: 1 1 4 − 3 4 1 1 4 − 3 4

Try It 4.177

Use a model to subtract. Draw a picture to illustrate your model.

1 1 3 − 2 3 1 1 3 − 2 3

Try It 4.178

1 1 5 − 4 5 1 1 5 − 4 5

Subtract Mixed Numbers with a Common Denominator

Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.

• Step 1. Rewrite the problem in vertical form.
• If the top fraction is larger than the bottom fraction, go to Step 3.
• If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.
• Step 3. Subtract the fractions.
• Step 4. Subtract the whole numbers.
• Step 5. Simplify, if possible.

Example 4.90

Find the difference: 5 3 5 − 2 4 5 . 5 3 5 − 2 4 5 .

Since the problem was given with mixed numbers, we leave the result as mixed numbers.

Try It 4.179

Find the difference: 6 4 9 − 3 7 9 . 6 4 9 − 3 7 9 .

Try It 4.180

Find the difference: 4 4 7 − 2 6 7 . 4 4 7 − 2 6 7 .

Just as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was given, so if we are given mixed numbers to subtract we will write the answer as a mixed number .

Subtract mixed numbers with common denominators as improper fractions.

Step 1. Rewrite the mixed numbers as improper fractions.

Step 2. Subtract the numerators.

Step 3. Write the answer as a mixed number, simplifying the fraction part, if possible.

Example 4.91

Find the difference by converting to improper fractions:

9 6 11 − 7 10 11 . 9 6 11 − 7 10 11 .

Try It 4.181

Find the difference by converting the mixed numbers to improper fractions:

6 4 9 − 3 7 9 . 6 4 9 − 3 7 9 .

Try It 4.182

4 4 7 − 2 6 7 . 4 4 7 − 2 6 7 .

Add and Subtract Mixed Numbers with Different Denominators

To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.

Example 4.92

Add: 2 1 2 + 5 2 3 . 2 1 2 + 5 2 3 .

Since the denominators are different, we rewrite the fractions as equivalent fractions with the LCD, 6 . 6 . Then we will add and simplify.

We write the answer as a mixed number because we were given mixed numbers in the problem.

Try It 4.183

Add: 1 5 6 + 4 3 4 . 1 5 6 + 4 3 4 .

Try It 4.184

Add: 3 4 5 + 8 1 2 . 3 4 5 + 8 1 2 .

Example 4.93

Subtract: 4 3 4 − 2 7 8 . 4 3 4 − 2 7 8 .

Since the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD 8 . 8 . Once in that form, we will subtract. But we will need to borrow 1 1 first.

We were given mixed numbers, so we leave the answer as a mixed number.

Try It 4.185

Find the difference: 8 1 2 − 3 4 5 . 8 1 2 − 3 4 5 .

Try It 4.186

Find the difference: 4 3 4 − 1 5 6 . 4 3 4 − 1 5 6 .

Example 4.94

Subtract: 3 5 11 − 4 3 4 . 3 5 11 − 4 3 4 .

We can see the answer will be negative since we are subtracting 4 4 from 3 . 3 . Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers.

Try It 4.187

Subtract: 1 3 4 − 6 7 8 . 1 3 4 − 6 7 8 .

Try It 4.188

Subtract: 10 3 7 − 22 4 9 . 10 3 7 − 22 4 9 .

ACCESS ADDITIONAL ONLINE RESOURCES

• Adding Mixed Numbers
• Subtracting Mixed Numbers

Section 4.6 Exercises

Practice makes perfect.

Model Addition of Mixed Numbers

In the following exercises, use a model to find the sum. Draw a picture to illustrate your model.

1 1 5 + 3 1 5 1 1 5 + 3 1 5

2 1 3 + 1 1 3 2 1 3 + 1 1 3

1 3 8 + 1 7 8 1 3 8 + 1 7 8

1 5 6 + 1 5 6 1 5 6 + 1 5 6

Add Mixed Numbers with a Common Denominator

In the following exercises, add.

5 1 3 + 6 1 3 5 1 3 + 6 1 3

2 4 9 + 5 1 9 2 4 9 + 5 1 9

4 5 8 + 9 3 8 4 5 8 + 9 3 8

7 9 10 + 3 1 10 7 9 10 + 3 1 10

3 4 5 + 6 4 5 3 4 5 + 6 4 5

9 2 3 + 1 2 3 9 2 3 + 1 2 3

6 9 10 + 8 3 10 6 9 10 + 8 3 10

8 4 9 + 2 8 9 8 4 9 + 2 8 9

In the following exercises, use a model to find the difference. Draw a picture to illustrate your model.

1 1 6 − 5 6 1 1 6 − 5 6

1 1 8 − 5 8 1 1 8 − 5 8

In the following exercises, find the difference.

2 7 8 − 1 3 8 2 7 8 − 1 3 8

2 7 12 − 1 5 12 2 7 12 − 1 5 12

8 17 20 − 4 9 20 8 17 20 − 4 9 20

19 13 15 − 13 7 15 19 13 15 − 13 7 15

8 3 7 − 4 4 7 8 3 7 − 4 4 7

5 2 9 − 3 4 9 5 2 9 − 3 4 9

2 5 8 − 1 7 8 2 5 8 − 1 7 8

2 5 12 − 1 7 12 2 5 12 − 1 7 12

In the following exercises, write the sum or difference as a mixed number in simplified form.

3 1 4 + 6 1 3 3 1 4 + 6 1 3

2 1 6 + 5 3 4 2 1 6 + 5 3 4

1 5 8 + 4 1 2 1 5 8 + 4 1 2

7 2 3 + 8 1 2 7 2 3 + 8 1 2

9 7 10 − 2 1 3 9 7 10 − 2 1 3

6 4 5 − 1 1 4 6 4 5 − 1 1 4

2 2 3 − 3 1 2 2 2 3 − 3 1 2

2 7 8 − 4 1 3 2 7 8 − 4 1 3

Mixed Practice

In the following exercises, perform the indicated operation and write the result as a mixed number in simplified form.

2 5 8 · 1 3 4 2 5 8 · 1 3 4

1 2 3 · 4 1 6 1 2 3 · 4 1 6

2 7 + 4 7 2 7 + 4 7

2 9 + 5 9 2 9 + 5 9

1 5 12 ÷ 1 12 1 5 12 ÷ 1 12

2 3 10 ÷ 1 10 2 3 10 ÷ 1 10

13 5 12 − 9 7 12 13 5 12 − 9 7 12

15 5 8 − 6 7 8 15 5 8 − 6 7 8

5 9 − 4 9 5 9 − 4 9

11 15 − 7 15 11 15 − 7 15

4 − 3 4 4 − 3 4

6 − 2 5 6 − 2 5

9 20 ÷ 3 4 9 20 ÷ 3 4

7 24 ÷ 14 3 7 24 ÷ 14 3

9 6 11 + 7 10 11 9 6 11 + 7 10 11

8 5 13 + 4 9 13 8 5 13 + 4 9 13

3 2 5 + 5 3 4 3 2 5 + 5 3 4

2 5 6 + 4 1 5 2 5 6 + 4 1 5

8 15 · 10 19 8 15 · 10 19

5 12 · 8 9 5 12 · 8 9

6 7 8 − 2 1 3 6 7 8 − 2 1 3

6 5 9 − 4 2 5 6 5 9 − 4 2 5

5 2 9 − 4 4 5 5 2 9 − 4 4 5

4 3 8 − 3 2 3 4 3 8 − 3 2 3

Everyday Math

Sewing Renata is sewing matching shirts for her husband and son. According to the patterns she will use, she needs 2 3 8 2 3 8 yards of fabric for her husband’s shirt and 1 1 8 1 1 8 yards of fabric for her son’s shirt. How much fabric does she need to make both shirts?

Sewing Pauline has 3 1 4 3 1 4 yards of fabric to make a jacket. The jacket uses 2 2 3 2 2 3 yards. How much fabric will she have left after making the jacket?

Printing Nishant is printing invitations on his computer. The paper is 8 1 2 8 1 2 inches wide, and he sets the print area to have a 1 1 2 1 1 2 -inch border on each side. How wide is the print area on the sheet of paper?

Framing a picture Tessa bought a picture frame for her son’s graduation picture. The picture is 8 8 inches wide. The picture frame is 2 5 8 2 5 8 inches wide on each side. How wide will the framed picture be?

Writing Exercises

Draw a diagram and use it to explain how to add 1 5 8 + 2 7 8 . 1 5 8 + 2 7 8 .

Edgar will have to pay $3.75 $3.75 in tolls to drive to the city.

ⓐ Explain how he can make change from a $10 $10 bill before he leaves so that he has the exact amount he needs.

ⓑ How is Edgar’s situation similar to how you subtract 10 − 3 3 4 ? 10 − 3 3 4 ?

Add 4 5 12 + 3 7 8 4 5 12 + 3 7 8 twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?

Subtract 3 7 8 − 4 5 12 3 7 8 − 4 5 12 twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/prealgebra/pages/1-introduction

• Authors: Lynn Marecek, MaryAnne Anthony-Smith
• Publisher/website: OpenStax
• Book title: Prealgebra
• Publication date: Sep 25, 2015
• Location: Houston, Texas
• Book URL: https://openstax.org/books/prealgebra/pages/1-introduction
• Section URL: https://openstax.org/books/prealgebra/pages/4-6-add-and-subtract-mixed-numbers

© Feb 9, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Fractions—Add and Subtract with Mixed Numbers

With our Fractions – Add and Subtract with Mixed Numbers lesson plan, students learn how to add and subtract mixed numbers using specific methods.

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. One of the optional additions to this lesson is to have students create addition or subtraction problems with mixed numbers to share with their classmates (including an answer key).

Description

Additional information, what our fractions—add and subtract with mixed numbers lesson plan includes.

Lesson Objectives and Overview: Fractions—Add and Subtract with Mixed Numbers teaches students methods for adding and subtracting mixed numbers.  At the end of the lesson, students will be able to add and subtract fractions with unlike denominators, including mixed numbers. 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 supplies you will need for this lesson are colored pencils, poster paper, and the handouts. To prepare for this lesson ahead of time, you can pair students for the activity, 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. One optional addition to the lesson activity is to have students vote for posters in different categories, like best poster, most colorful, and neatest. If you’d like to add another activity to this lesson, you can have students create addition or subtraction problems with mixed numbers to share with their classmates (including an answer key). Finally, your students can use hands-on manipulatives to enhance their understanding of the concept of borrowing or regrouping a whole number.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. It notes that you can use this lesson along with other lessons related to fractions and mixed numbers. 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 WITH MIXED NUMBERS LESSON PLAN CONTENT PAGES

Adding/subtracting fractions.

The Fractions—Add and Subtract with Mixed Numbers lesson plan includes three content pages. The lesson begins by reminding students that they’ve already learned how to add and subtract fractions with both like and unlike denominators. To do this, you first need to find common denominators (also called a lowest common denominator or LCD). We actually have two main strategies for add and subtracting fractions with unlike denominators.

The first strategy is to find the lowest common denominator. To solve the example problem 3/4 + 5/6 using this method, we first need to identify the LCD. In this case, the LCD is 12. We then use the LCD to create equivalent fractions. 3/4 becomes 9/12 and 5/6 becomes 10/12. The new equation is 9/12 + 10/12. The final step is to add the equivalent fractions and change the sum or difference to a mixed number, reducing if necessary. 9/12 + 10/12 = 19/12 = 1 7/12.

The second strategy is to cross multiply. Using the same example problem, the first step is to multiply the two denominators, which will become the new denominator (4 x 6 = 24). We then cross multiply the numerators and denominators (3 x 6 and 4 x 5). We then add them together to find the new numerator. 3 x 6 = 18 and 4 x 5 = 20. 18 + 20 = 38, so the new fraction is 38/24. Finally, we reduce as needed. 38/24 = 19/12 = 1 7/12.

We can use either of these strategies to add or subtract fractions with unlike denominators. We can also use these strategies when adding or subtracting fractions with mixed numbers or adding or subtracting mixed numbers with other mixed numbers.

Fractions and Mixed Numbers

Next, the lesson discusses how to add and subtract fractions with mixed numbers. A mixed number is a fraction that includes a whole number. The first addition strategy for mixed numbers is to add the whole numbers and fractions separately. The lesson includes an example problem to illustrate this strategy: 1 1/2 + 2 3/4. The first step is to add the whole numbers (1 + 2 = 3). Next, we add the fractions using one of the strategies from the first part of the lesson. In this example, we add 1/2 + 3/4 and end up with 1 1/4. Finally, we add the sum of the fractions to the whole numbers. In this case, we add 3 + 1 = 4. We add the fraction to the whole number for a final sum of 4 1/4.

The next strategy shows how to subtract whole numbers and fractions. The example problem is 2 3/4 – 1 1/2. First, we change the mixed numbers to improper fractions. 2 3/4 becomes 11/4 and 1 1/2 becomes 3/2. Finally, we subtract the improper fractions using one of the strategies that we’ve already learned. The final answer is 1 1/4. This is a good method to use when you don’t have to borrow or regroup numbers. The final two subtraction strategies cover situations in which you have to borrow or regroup.

The next strategy shows another way to subtract whole numbers and fractions, using the example 15 – 8 2/3. The first step is to borrow 1 from the whole number (or regroup), creating a fraction with the same denominator as the mixed number. In this example, we borrow 1 from 15 and regroup. 3/3 = 1, so 15 = 14 3/3. Next, we use the regrouped number to subtract; the problem is now a subtraction problem with like denominators! 14 3/3 – 8 1/3 = 6 2/3.

The final strategy shows a way to subtract mixed numbers from mixed numbers, using the example 150 1/2 – 80 2/3. The first step is to borrow 1 or regroup from the whole number using the same method described previously. 2/2 = 1, so 150 = 149 2/2 + 1/2 = 149 3/2. Next, we use the regrouped number to subtract: 149 3/2 – 80 2/3. We have to find the lowest common denominator (in this problem, it’s 6) and find equivalent fractions. We can then subtract normally! The final answer is 69 5/6.

You can use all of these strategies to add or subtract mixed numbers. The strategy you choose will depend on the problem. One important note is that you have to find a common denominator for all problems with unlike denominators. You must also know how to find equivalent fractions and how to multiply correctly!

FRACTIONS—ADD AND SUBTRACT WITH MIXED NUMBERS LESSON PLAN WORKSHEETS

The Fractions—Add and Subtract with Mixed Numbers 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.

POSTER ACTIVITY WORKSHEET

Students will work with a partner to complete the activity worksheet. Each pair of students will create a poster, half of which will show a strategy for adding two mixed numbers, and the other half of which will show a different strategy for subtracting two mixed numbers with regrouping or borrowing. Students will use text, pictures, arrows, labels, and more on their poster. The poster should clearly show someone how to add and subtract mixed numbers. The worksheet includes space that students can use for a rough draft of their poster.

Students can also work either alone or in larger groups for this activity.

SOLVING PROBLEMS PRACTICE WORKSHEET

The practice worksheet asks students to solve 15 problems using one or more of the strategies that they learned during the lesson.

FRACTIONS—ADD AND SUBTRACT WITH MIXED NUMBERS HOMEWORK ASSIGNMENT

For the homework assignment, students will first read, solve, and explain two word problems where they need to add or subtract with mixed numbers. They will also solve three problems that involve mixed numbers.

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.

Related products

Lewis and Clark Expedition

Careers: Archaeologist

Careers: Astronomer

Killer Bees

Make your life easier with our lesson plans, stay up-to-date with new lessons.

• Lesson Plans
• For Teachers

© 2024 Learn Bright. All rights reserved. Terms and Conditions. Privacy Policy.

• Sign Up for Free

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice
• Measurement
• Factoring & prime factors
• Proportions
• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

• Fractions: add / subtract

Adding mixed numbers

Download & Print Only $4.90

Fractions worksheets: Adding mixed numbers (unlike denominators)

Below are six versions of our grade 6 math worksheet on adding mixed numbers. The fractional part of the addends will typically have unlike denominators between 2 and 12. These fraction worksheets are pdf files .

These worksheets are available to members only.

Join K5 to save time, skip ads and access more content. Learn More

More fractions worksheets

Explore all of our fractions worksheets , from dividing shapes into "equal parts" to multiplying and dividing improper fractions and mixed numbers.

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

• Forgot Password?

Grade 5 - 6.6 Add and Subtract Mixed Numbers

• Google Slides™

Also included in

Description

This is a google slideshow that follows the GoMath book for 5th grade. The lesson gives a section for the teacher to lead a class and a section for students to do independently.

Questions & Answers

Matthew lieber.

• We're hiring
• Help & FAQ
• Privacy policy
• Student privacy
• Terms of service
• Tell us what you think

• Texas Go Math
• Big Ideas Math
• Engageny Math
• McGraw Hill My Math
• enVision Math
• 180 Days of Math
• Math in Focus Answer Key
• Math Expressions Answer Key
• Privacy Policy

McGraw Hill My Math Grade 5 Chapter 9 Lesson 11 Answer Key Add Mixed Numbers

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 9 Lesson 11 Add Mixed Numbers  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 9 Lesson 11 Add Mixed Numbers

Math in My World

Guided Practice

Independent Practice

Estimate, then add. Write each sum in simplest form.

Algebra Find each unknown.

Question 12. 14\(\frac{19}{20}\) + 8\(\frac{1}{4}\) = k k = _____ Answer: The above-given fractions: 14 19/20 + 8 1/4 = k Here the denominators are not the same. So we have to find the equivalent denominators. – Find the common denominators: k = 14 + 8 + 19/20 + 1/4 20 is the least common multiple of denominators 20 and 4. Use it to convert to equivalent fractions with this common denominator. k = 22 + ( 19 + 5)/20 k = 22 + 24/20 24/20 is not simplified because 4 is a common factor for 24 and 20 24/20: if we divide by 4 then we get 6/5 6/5 is an improper fraction. So we have to convert it into a mixed fraction. 6 ÷ 5 = 1   remainder 1. The mixed fraction is 1 1/5 k = 22 + 1 1/5 k = 23 1/5

Question 13. 16\(\frac{11}{12}\) + 5\(\frac{2}{3}\) = d d = _____ Answer: The above-given mixed fraction: 16 11/12 + 5 2/3 = d Here the denominators are not the same. So we have to find the equivalent denominators. – Find the common denominators: d = 16 + 5 + 11/12 + 2/3 12 is the least common multiple of denominators 12 and 3. Use it to convert to equivalent fractions with this common denominator. d = 21 + (11 + 8)/12 d = 21 + 19/12 19/12 is an improper fraction so we have to convert it into a mixed fraction. 19 ÷ 12 = 1 remainder 7 This can be written as 1 7/12 d = 21 + 1 7/12 d = 22 7/12.

Problem Solving

Question 14. Zita made 1\(\frac{5}{8}\) quarts of punch. Then she made 1\(\frac{7}{8}\) more quarts. How much punch did she make in all? Answer: The above-given: The number of quarts of punch Zita made = 1 5/8 The number of quarts of more punch she made = 1 7/8 The total punch she makes = p p = 1 5/8 + 1 7/8 p = 1 + 1 + 5/8 + 7/8 p = 2 + 12/8 p = 2 + 3/2 p = 2 3/2 Therefore, the total punch is 2 3/2 quarts.

Question 15. Find five and two-eighths plus three and six-eighths. Write in words in simplest form. Answer: This can be written as: 5 2/8 + 3 6/8 Now simplify the equation: 5 + 3 + 2/8 + 6/8 As the denominators are the same, so we can add directly. = 8 + 8/8 = 8 + 1 = 9 In word form, nine.

HOT Problems

Question 18. ? Building on the Essential Question How can equivalent fractions help when adding mixed numbers? Answer: – It can help by when finding the LCD (Least Common Denominator) you find the least number they have in common then that number is your equivalent fraction. * The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions.

McGraw Hill My Math Grade 5 Chapter 9 Lesson 11 My Homework Answer Key

Question 1. 2\(\frac{1}{10}\) + 5\(\frac{7}{10}\) = ____ Answer: The above-given mixed fractions: 2 1/10 + 5 7/10 Now simplify the equation: = 2 + 5 + 1/10 + 7/10 = 7 + 1/10 + 7/10 as the denominators are the same so we can directly add the fractions. = 7 + 8/10 8/10 is not simplified because 2 is a common factor of 8 and 10. 8/10 = if we divide by 2 then we get 4/5 = 7 + 4/5 * A mixed fraction a b/c can also be written as a + (b/c). = 7 4/5. Therefore, 2\(\frac{1}{10}\) + 5\(\frac{7}{10}\) = 7 4/5.

Question 2. 9\(\frac{3}{4}\) + 8\(\frac{3}{4}\) = ____ Answer: The above-given mixed fractions: 9 3/4 + 8 3/4 = 9 + 8 + 3/4 + 3/4 = 17 + 6/4 6/4 is divided by 2 because 2 is a common factor of 6 and 4. 6/4 = 3/2 = 17 + 3/2 3/2 is an improper fraction so convert it into a mixed fraction. 3/2 = 1 remainder = 1 3/2 in the mixed fraction is 1 1/2 Finally, 17 + 1 1/2 = 18 1/2 Therefore, 9\(\frac{3}{4}\) + 8\(\frac{3}{4}\) = 18 1/2.

Question 3. 3\(\frac{5}{8}\) + 6\(\frac{1}{2}\) = ____ Answer: The above-given mixed fraction: 3 5/8 + 6 1/2 = 3 + 6 + 5/8 + 1/2 Here the denominators are not the same. So we have to find the equivalent denominators. – Find the common denominators: = 9 + 5/8 + 1/2 8 is the least common multiple of denominators 8 and 2. Use it to convert to equivalent fractions with this common denominator. = 9 + ( 5 + 4)/8 = 9 + 9/8 9/8 is an improper fraction, so convert it into a mixed fraction. 9/8 = 1 remainder = 1 The mixed fraction can be written as 1 1/8. = 9 + 1 1/8 = 10 1/8 Therefore, 3\(\frac{5}{8}\) + 6\(\frac{1}{2}\) = 10 1/8.

Question 4. 1\(\frac{1}{12}\) + 4\(\frac{5}{12}\) = ____ Answer: The above-given mixed fractions: 1 1/12 + 4 5/12 Here denominators are the same so we can add fractions directly. = 1 + 4 + 1/12 + 5/12 = 5 + 6/12 = 5 + 1/2 * A mixed fraction a b/c can also be written as a + (b/c). = 5 1/2 Therefore, 1\(\frac{1}{12}\) + 4\(\frac{5}{12}\) = 5 1/2.

Question 5. 11\(\frac{3}{5}\) + 6\(\frac{4}{15}\) = ____ Answer: The above-given fractions: 11 3/5 + 6 4/15 = 11 + 6 + 3/5 + 4/15 = 17 + 3/5 + 4/15 Here the denominators are not the same. So we have to find the equivalent denominators. – Find the common denominators: 15 is the least common multiple of denominators 5 and 15. Use it to convert to equivalent fractions with this common denominator. = 17 + (9 + 4)/15 = 17 + 13/15 * A mixed fraction a b/c can also be written as a + (b/c). = 17 13/15. Therefore, 11\(\frac{3}{5}\) + 6\(\frac{4}{15}\) = 17 13/15.

Question 6. 9\(\frac{1}{2}\) + 12\(\frac{11}{20}\) = ____ Answer: The above-given mixed fractions: 9 1/12 + 12 11/20 9 + 12 + 1/12 + 11/20 = 21 + 1/12 + 11/20 Here the denominators are not the same. So we have to find the equivalent denominators. – Find the common denominators: 60 is the least common multiple of denominators 12 and 20. Use it to convert to equivalent fractions with this common denominator. = 21 + (5 + 33)/60 = 21 + 38/60 38/60 is not simplified because 2 is a common factor of 38 and 60 38/60 is divided by 2 then we get 19/30 = 21 + 19/30 * A mixed fraction a b/c can also be written as a + (b/c). = 21 19/30.

Question 7. A flower is 9\(\frac{3}{4}\) inçhes tall. In one week, it grew 1\(\frac{1}{8}\) inches. How tall is the flower at the end of the week? Write in simplest form. Answer: The above-given: The number of inches is a flower tall = 9 3/4 The number of inches it grew = 1 1/8 The number of inches a flower is tall at the end of the week = x x = 9 3/4 + 1 1/8 x = 9 + 1 + 3/4 + 1/8 x = 10 + 3/4 + 1/8 Here the denominators are not the same. So we have to find the equivalent denominators. – Find the common denominators: 8 is the least common multiple of denominators 4 and 8. Use it to convert to equivalent fractions with this common denominator. x = 10 + (6 + 1)/8 x = 10 + 7/8 x = 10 7/8 Therefore, a flower grows 10 7/8 inches at the end of the week.

Question 8. Find ten and three-sevenths plus eighteen and two-sevenths. Write in words in simplest form. Answer: The above-given: 10 3/7 + 18 2/7 10 + 18 + 3/7 + 2/7 = 28 + 3/7 + 2/7 here the denominators are the same so we can directly add the fractions. = 28 + 5/7 = 28 5/7. In word form, we can write as twenty-eight and five-sevenths.

Question 9. Mathematical PRACTICE 6 Explain to a Friend Connor is filling a 15-gallon wading pool. On his first trip, he carried 3\(\frac{1}{12}\)– gallons of water. He carried 3\(\frac{5}{6}\) gallons on his second trip and 3\(\frac{1}{2}\) gallons on his third trip. Suppose he carries 5 gallons on his next trip. Will the pool be filled? Explain. Answer: The above-given: The number of gallons a wading pool = 15 The number of gallons of water he carried on the first trip = 3 1/12 The number of gallons of water he carried on the second trip = 3 5/6 The number of gallons of water he carried on the third trip = 3 1/12 if he carries 5 gallons on the fourth trip, is the pool filled = x x = 3 1/12 + 3 5/6 + 3 1/12 x = 3 + 3 + 3 + 1/12 + 5/6 + 1/12 x = 9 + 2/12 + 5/6 x = 9 + 1/6 + 5/6          { 2/12 = 1/6   (divided by 2) } Here the denominators are the same so we can add the fractions directly. x = 9 + 6/6 x = 9 + 1 x = 10 up to three trips 10 gallons are carried by him. On the next trip, he takes 5 gallons: 10 + 5 = 15 gallons. Therefore, the warden pool is filled with 15 gallons of water.

Test Practice

Leave a Comment Cancel Reply

You must be logged in to post a comment.