Multiplying and dividing fractions · Year 7
In Year 7 you learn: dividing by a fraction.
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).
- Multiplying by a fraction less than 1 makes a number smaller; dividing by it makes it bigger.
Worked examples
Example 1
Work out 2 1/2 × 1 3/5.
Answer: 4
Example 2
How many 3/8-litre cups can be filled from a 4 1/2-litre jug?
Answer: 12 cups