Multiplying and dividing fractions · Usually met around P5
Mixed numbers, and three numbers multiplied or divided
Mixed to improper; ÷ becomes × the reciprocal.
How to do it
Method
Mixed to improper; ÷ becomes × the reciprocal
2 13 × 314 = 73 × 314 = 12
Another way
Cancel all at once
34 × 29 ÷ 16 = 34 × 29 × 6 = 1
In full
Change mixed numbers to improper fractions first: 2 13 = 73. Dividing by a fraction is multiplying by its reciprocal: ÷ 34 is × 43. For three numbers, way 1: work left to right, two at a time. Way 2: turn every ÷ into × the reciprocal, write one long product, cancel tops against bottoms all at once, then multiply: 34 × 29 ÷ 16 = 34 × 29 × 61 = 1. Cancelling first keeps the numbers small.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
3 12 × 4 = □ (an improper fraction is fine)
Answer in simplest form
Show the answer and working
Answer: 14
3 12 = 72, and 72 × 4 = 141.
Example 2
2 34 ÷ 19 = □ (an improper fraction is fine)
Answer in simplest form
Show the answer and working
Answer: 994
2 34 = 114; ÷ 19 is × 91: 994.
Example 3
To work out 5 310 × 12, what should 5 310 be written as first?
- A. 810
- B. 5310
- C. 1510
- D. 4710
Choose the right answer
Show the answer and working
Answer: B. 5310
5 310 = (5 × 10 + 3)/10 = 5310.
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