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# Multiply A Fraction by A Whole Number

## Key Concepts

• Solve constant speed problems
• Solving unit-price problems
• Using an equation to represent unit rate problems

## Multiply fractions and whole numbers

Model: Standard multiplication of whole numbers and fractions

1. Hal spent ¾ hour each day for 7 days. How much total time did he spend reading?

Multiply to find the number of fourths

7 x 3/4 = 7 x 3 x 1/4

= 21 x 1/4 = 21/4

Rewrite as a mixed fraction number

21/4 = 5 1/4

Hal spent 5 1/4 hours of reading.

1. Explain how 3/4 x 7, 7 x 3/4  and 3 x 7/4  are all related?

Given that, prove

3/4 x 7 = 7 x 3/4  = 3 x 7/4

Case 1:

3/4 x 7 = 1/4 x 3 x 7

= 1/4 x 21

= 21/4

Case 2:

7 x 3/4

= 7 x 3 x 1/4

= 21 x 1/4

= 21/4

Case 3:

3 x 7/4

= 3 x 7 x 1/4

= 21 x 1/4

= 21/4

So,

3/4 x 7 = 7 x 3/4

= 3 x 7/4

= 21/4

### Practice

1. 4/5 x 500

Solution:

4/5 x 500 = 2000/5

4/5 x 500=400

2. 5 x 2/3

Solution:

5 x 2/3

= 5 X 2/3

= 10/3 x 2/3

= 3 1/3

3. 9/10 x 25

Solution:

9/10 x 25 = 9 X 25/10

= 225/10

= 9/10 x 25  = 22.5 or 22

5/10 or 12

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