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Multiply A Fraction by A Whole Number

Sep 29, 2022
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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 fractions and whole numbers

Multiply to find the number of fourths 

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

2 1/4

= 21 x 1/4 = 21/4

Rewrite as a mixed fraction number 

parallel

21/4 = 5 1/4 

Hal spent 5 1/4 hours of reading. 

hal
  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: 

parallel

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

Comments:

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