Multiplying and dividing fractions · Year 9
In Year 9 you get fluent with: mixed numbers and reciprocals.
Multiplying fractions is the simplest fraction operation: multiply the tops, multiply the bottoms. “Of” means multiply, so 1/2 of 3/4 is 3/8. Dividing by a fraction asks “how many of these fit?”, and is done by multiplying by its reciprocal.
Key facts
- a/b × c/d = (a × c)/(b × d). Simplify at the end, or cancel common factors first.
- A whole number n is n/1: 3/4 × 8 = 24/4 = 6.
- The reciprocal of a/b is b/a; the reciprocal of 5 is 1/5.
- To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c (keep, change, flip).
- Change mixed numbers into improper fractions before multiplying or dividing.
- Multiplying by a fraction less than 1 makes a number smaller; dividing by it makes it bigger.
Worked examples
Example 1
Work out 3/4 ÷ 2/5.
Answer: 1 7/8