Use Models to Add Mixed Numbers

Key Concepts

• Using models to add mixed numbers
• Adding mixed numbers

Introduction 

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

Example 1: 

You and your friend went to a pizza shop. You ate 1 pizza, and your friend ate 1/2 pizza. It means you and your friend ate 3/2 pizza in total. 

3/2 is equal to 1 1/2. 

If you observe the above example, 3/2 is called fraction and 1 1/2 is called mixed number. 

Using Models to Adding Mixed Numbers 

Example 1: 

Mary worked 2 3/4 hours on Monday and 1 1/2 hours on Tuesday. How many hours did she work in all on Monday and Tuesday? 

Solution: 

Step 1: 

Add the fractional parts first. 

To do this, we need to rename the fractional parts as equivalent fractions with a like denominator. 

3/4 + 2/4 = 5/4

Rename 5/4 as 1 1/4. 

Step 2: 

Add the whole number parts. 

2 + 1 = 3 

Then add the sum of the functional parts. 

3 + 1 1/4 = 4 1/4

So, 2 3/4 + 1 1/2 = 4 1/4

The total number of hours worked in all on Monday and Tuesday is 4 1/4

Adding Mixed Numbers 

Example 1: 

Joaquin used two types of flours in a muffin recipe. How much flour did he use in all? Solve it in any way you choose. 

Solution: 

Step 1: 

From the given ingredients, we can understand that Joaquin used 1 1/2 c of whole wheat flour and 4 2/3 c of buckwheat flour. 

So, we need to add 1 1/2 and 4 2/3 to find the total flour used. 

Write equivalent fractions with a common denominator. 

1 1/2 = 1 3/6

4 2/3 = 4 4/6

Step 2: 

Add the fractions. 

Step 3: 

Add the whole numbers. 

1 1/2 = 1 3/6

4 2/3 = 4 4/6

___________ 

5 7/6

Rewrite

7/6 as a mixed number. 

5 7/6 = 5 + 1 1/6 = 6 1/6

The total flour used by Joaquin was 6 1/6c. 

Example 2: 

Arnie has 1 1/2 apple pies with him. Louise has 2 1/3 apple pies with her. They mixed their apple pies together. They are wondering about the total apple pies they have with them. Solve it in any way you choose. 

Solution: 

Step 1: 

Add 1 1/2 and 2 1/3 to find the total apple pies. 

Write equivalent fractions with a common denominator. 

1 1/2 = 1 3/6

2 1/3 = 2 2/6

Step 2: 

Add the fractions. 

1 1/2 = 1 3/6

2 1/3 = 2 2/6

_____________ 

5/6

Step 3: 

Add the whole numbers. 

1 1/2 = 1 3/6

2 1/3 = 2 2/6

_____________ 

3 5/6

The total apple pies are 3 5/6

Exercise

• Use fraction strips and find the sum.

• 2 1/10 + 1 3/5
• 4 3/5 + 3 7/10

• Use fraction strips and find the sum.

• 1 7/8 + 5 1/4
• 3 2/5 +1 9/10

• Lindsey used 1 1/4 gallons of tan paint for the ceiling and 4 3/8 gallons of green paint for the walls of her kitchen. How much paint did Lindsey use in all? Use fraction strips to help.
• Paul said, “I walked 2 1/2 miles on Saturday and 2 3/4 miles on Sunday.” How many miles is that in all?
• Estimate and then find the sum.

1 7/8 = 1 ?/8

+ 1 1/4 = 1 ?/8

________________

• Estimate and then find the sum.

6 5/12 + 4 5/8

• What is the missing number in the following equation?

3 1/3 + 4/? = 4 2/15

• After a party, there were 1 1/4 quesadillas left on one tray and 2 3/6 quesadillas left on another tray. How many quesadillas were left?
• James wants to send two gifts by mail. One package weighs 2 3/4 pounds. The other package weighs 1 3/6 pounds. What is the total weight of the packages?
• Louise started from one point and reached another point. Use the map to find the distance from the start to the end of the trail.

Concept Map

What have we learned

• Adding mixed numbers using models
• Adding mixed numbers