Use Models to Subtract Mixed Numbers

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

Concept Map 

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