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
- 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.
- 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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