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# Use Models to Subtract Mixed Numbers

Sep 29, 2022

## Key Concepts

• Using models to subtract mixed numbers
• Subtract mixed numbers
• Addition and subtraction of mixed numbers in problems

### Introduction

In this chapter, we will learn about subtraction of mixed numbers using models.

Example 1:

You and your friend went to pizza shop. You ordered 4 pizzas.  You and your friend could eat only 2 1/2

pizzas. How much pizza is left?

Solution:

### Using models to subtract mixed numbers

Example 1:

James bought 3 1/2 pounds of butter and 2 1/4 pounds of cheese. He used 1 1/2 pounds of cheese to make macaroni and cheese. How much cheese does she have left?

Solution:

Step 1:

If the fraction you will be subtracting is greater than the fraction part of the number you model, rename 1 whole.

Step 2:

Use your renamed model to cross out the number that you are subtracting, 1 2/4

There are 3/4 left.

So, 2 1/4 – 1 1/2 = 3/4.

### Subtract Mixed Numbers

Example 1:

William walks 2 1/8 miles to his aunt’s house. He has already walked 3/4 mile. How much farther does he have to go? Solve this problem any way you choose.

Solution:

Step 1:

The total distance is 2 1/8 miles.

William 3/4 mile.

So, to find the remaining distance, we need to subtract 3/4 from 2 1/8.

To do this, we need to write equivalent fractions with a common denominator.

Since, 6/8 >1/8, you can rename 1 as 8/8 to subtract.

Step 2:

Step 3:

Subtract the fractions. Then subtract the whole numbers.

### Add and Subtract Mixed Numbers

Example 1:

Benjamin has 15 5/6 feet of wrapping paper. He uses 4 1/3 feet for his daughter’s present and 5 3/8 feet for his niece’s present. How much wrapping paper does Benjamin has left? Solve this problem any way you choose.

Solution:

Step 1:

Benjamin used 4 1/3 feet for his daughter’s present.

Benjamin used 5 3/8 feet for his niece’s present.

So, the total length of wrapping paper used was,

Step 2:

Subtract the amount of paper used from the total length of paper.

## Exercise

• Use fraction strips and find the difference of 12 3/4 and 9 5/8
• Find the missing number in the following equation.

12 1/2 – 10 11/2 = 1 7/?

• Elijah and Ethan volunteered at an animal shelter a total of 9 5/6 hours. Clara worked for 4 1/3 hours. How many hours did Ethan work? You can use fraction strips to solve this problem.
• Jackson lives 2 5/6 blocks away from his best friend. His school is 4 1/3 blocks away in the same direction. If he stops at his best friend’s house first, how much farther do they have to walk to school?
• Estimate and then find the difference.

3 1/2 = 3 ?/6

– 1 1/3 = 1 ?/6

• Estimate and then find the difference.

10 5/12 – 4 7/8

• Jack used the model to find5/12 – 7/12. Did Jack model the problem correctly? Explain.
If not, show how the problem should have been modeled
• Choose the correct number from the box below to complete the subtraction sentence
that follows.

2 4 5 10 15

14 1/10 – 3 1/? = 10 3/5

• Find the sum or difference

5 1/9

2 2/3

______

2 1/4

+ 8 2/3

______

• Do the operation in the parentheses first

(2 5/8 + 2 1/2) – 4 2/3

### What have we learned

• Calculate the subtraction of mixed numbers using models
• Calculate the subtraction of mixed numbers
• Find addition and subtraction of mixed numbers to solve problems

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