## 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 add 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

### Add 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