Multiplying and dividing fractions · Year 6
In Year 6 you learn: multiplying a fraction by a whole number, multiplying fractions, and dividing fractions by whole numbers.
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.
- Multiplying by a fraction less than 1 makes a number smaller; dividing by it makes it bigger.
Worked examples
Example 1
Work out 2/3 × 9/10.
Answer: 3/5
Example 2
Work out 2 1/2 × 1 3/5.
Answer: 4
Example 3
How many 3/8-litre cups can be filled from a 4 1/2-litre jug?
Answer: 12 cups