## Introduction:

In this chapter, we will learn about rounding a mixed number to the nearest whole number, adding and subtracting mixed numbers.

Let us understand mixed numbers,

A mixed number is a combination of a whole number and a proper fraction represented together. It generally represents a number between any two whole numbers.

### Example 1:

### Parts of a mixed number:

A mixed number is formed by combining three parts. They are,

- A whole number
- A numerator
- A denominator

## Using number line for rounding of the fractions

### Example 1:

After the class pizza party, there were 1×5/6 cheese pizzas and 2×5/6 vegetarian pizzas left over. How many pizzas were left over in total after the party?

### Solution:

Use a number line to round fractions and mixed numbers to the nearest whole number.

So, 1×5/6 + 2×5/6 = 2 + 3, or 5

5 pizzas were left over after the class party.

## Addition by rounding the fractions

### Example 1:

After the class pizza party, there were 1×5/6 cheese pizzas and 2×5/6 vegetarian pizzas left over. How many pizzas were left over in total after the party?

### Solution:

Use a number line to round fractions and mixed numbers to the nearest whole number.

Round each fraction as per the benchmark.

1×5/6 is close to 2.

2×5/6 is close to 3.

So, 1×5/6 2×5/6 is about 2 + 3 = 5.

### Example 2:

James has five cups of strawberries. He wants to use 1×3/4 cups of strawberries for a fruit salad and 3×1/2 cups for jam. Does James have enough strawberries to make both recipes? Solve this problem any way you choose.

### Solution:

Round each fraction as per the benchmark.

1×3/4 is close to 2.

So, 1×3/4 + 3×1/2 is about 2 + 3×1/2 = 5×1/2.

The total cups of strawberries required to make both fruit salad and jam are 5×1/2.

Hence, James does not have enough strawberries to make both recipes.

## Subtraction by rounding the fractions

### Example 1:

Ron used 2×2/5 liters of paint from a tin of 5×7/8 liter. To color the walls of his room, what fraction of paint is still left in the tin?

### Solution:

Round each fraction as per the benchmark.

5×7/8 is close to 6.

2×2/5 is close to 2.

So, 5×7/8 – 2×2/5 is about 6 – 2 = 4.

## Exercise:

- Round the mixed numbers to their nearest whole numbers.

a. 2×3/4 b. 1×5/7 c. 2×3/10

- Use the number line to round the mixed numbers to the nearest whole numbers.

a. 11×4/6 b. 11×2/8

- Use the number line to round the mixed numbers to the nearest whole numbers.

a. 11×8/12 b. 11×4/10

- Estimate the sum.

a. 2×2/3 + 6×7/12 b. 12×1/3 + 2×1/4

- Estimate the difference.

a. 2×1/8 – 5/7 b. 10×5/6 – 2×3/8

- Estimate the sum.

a. 2×1/3 + 3×3/4 + 6×1/9 b. 12×1/3 + 2×2/3

- Estimate the difference.

a. 9×11/12 – 4×3/8 – 1×7/10 b. 4×3/4 – 2×2/3

- A man pours 2×2/8 gallons of paint from a bucket into a tray. After he finishes pouring, there are 1×1/4 gallons of paint left in his bucket. How much paint did the man pour into the tray?
- Michelle ran for 1×1/5 h and then walked for 2×1/4 h. For how long did she travel?
- Ronald and Stephen race to see who can collect the most tennis balls on the ground. Ronald has collected 5×1/3 sets. Stephen has collected 4×3/4 sets. Who has collected more sets? How much more?

## Concept map:

## What have we learned:

- Understand parts of a mixed number.
- Use number line and round the fraction.
- Add and subtract by rounding the fractions

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