Stage 8 · Fractions & decimals
Multiplying fractions
Tops times tops, bottoms times bottoms.
How to do it
Method
Tops times tops, bottoms times bottoms
23 × 34 = 612 = 12
One more example
2 × 38 = 68 = 34
In full
A fraction times a fraction: tops times tops, bottoms times bottoms, then simplify: 23 × 34 = 612 = 12. Or cancel first for smaller numbers: in 23 × 34 the 3 on top and the 3 below cancel, and the 2 on top and the 4 below both ÷ 2, leaving 12. A fraction times a whole number: the whole number times the top, the bottom unchanged: 2 × 38 = 68 = 34; 12 × 34 is 34 of 12: 12 ÷ 4 = 3, 3 × 3 = 9. Cancel before or simplify after — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
12 × 12
Show the answer and working
Answer: 12 × 12 = 6
12 × 12: that's 12 of 12, 12 ÷ 2 = 6, 6 × 1 = 6
Example 2
24 × 56
Show the answer and working
Answer: 24 × 56 = 20
24 × 56: that's 56 of 24, 24 ÷ 6 = 4, 4 × 5 = 20
Example 3
17 × 12
Answer in simplest form
Show the answer and working
Answer: 17 × 12 = 114
17 × 12: tops times tops, 1 × 1 = 1; bottoms times bottoms, 7 × 2 = 14 → 114, already in simplest form
Example 4
14 × 512
Answer in simplest form
Show the answer and working
Answer: 14 × 512 = 548
14 × 512: tops times tops, 1 × 5 = 5; bottoms times bottoms, 4 × 12 = 48 → 548, already in simplest form
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