Stage 8 · Fractions & decimals
Dividing fractions
Dividing by a fraction: flip it and multiply.
How to do it
Method
Dividing by a fraction: flip it and multiply
34 ÷ 38 = 34 × 83 = 2412 = 2
One more example
6 ÷ 34 = 6 × 43 = 243 = 8
In full
Dividing by a number is the same as multiplying by its reciprocal: swap the divisor's top and bottom, then multiply the fractions. 34 ÷ 38 = 34 × 83 = 2412 = 2; cancelling first is quicker: the 3 on top and the 3 below cancel, and the 8 and the 4 both ÷ 4, leaving 2. A fraction ÷ a whole number: the whole number's reciprocal is 1 over it, 34 ÷ 3 = 34 × 13 = 312 = 14. A whole number ÷ a fraction: 6 ÷ 34 = 6 × 43 = 243 = 8. Give the answer in simplest form. When the two fractions share a denominator you can also just divide the tops: 34 ÷ 38 = 68 ÷ 38 = 6 ÷ 3 = 2 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
10 ÷ 512
Show the answer and working
Answer: 10 ÷ 512 = 24
10 ÷ 512: multiply by the reciprocal 125: 10 × 12 = 120, 120 ÷ 5 = 24
Example 2
14 ÷ 9
Answer in simplest form
Show the answer and working
Answer: 14 ÷ 9 = 136
14 ÷ 9: dividing by 9 is multiplying by 19: the top stays, the bottom 4 × 9 = 36 → 136, already in simplest form
Example 3
111 ÷ 7
Answer in simplest form
Show the answer and working
Answer: 111 ÷ 7 = 177
111 ÷ 7: dividing by 7 is multiplying by 17: the top stays, the bottom 11 × 7 = 77 → 177, already in simplest form
Example 4
12 ÷ 18
Show the answer and working
Answer: 12 ÷ 18 = 4
12 ÷ 18: dividing by 18 is multiplying by its reciprocal 81: 12 × 81, tops 1 × 8 = 8, bottoms 2 × 1 = 2 → 82; simplify, dividing top and bottom by 2: 8 ÷ 2 = 4, 2 ÷ 2 = 1 → 4
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