Multiplying and Dividing Fractions

Grade 3

Multiplying fractions — the easy one

Multiplication is the most straightforward operation with fractions. No common denominator needed — just multiply the tops together and the bottoms together.

a/b × c/d = (a×c) / (b×d)
Before multiplying, check if you can cancel (simplify) across the fractions. Divide a numerator and a denominator by a common factor before you multiply — it keeps the numbers smaller.
EXAMPLE
Work out ³⁄₄ × ⁸⁄₉.
Cancel first: 3 and 9 share a factor of 3 → ¹⁄₄ × ⁸⁄₃. Then 4 and 8 share a factor of 4 → ¹⁄₁ × ²⁄₃. Multiply: 1 × 2 = 2 and 1 × 3 = 3. Answer: ²⁄₃.

Dividing fractions — flip and multiply

Dividing by a fraction is the same as multiplying by its reciprocal — its upside-down version. The method is sometimes called keep-change-flip (or KFC):

Keep the first fraction → Change ÷ to × → Flip the second fraction

Then just multiply as normal.

EXAMPLE
Work out ⁵⁄₆ ÷ ²⁄₃.
Keep ⁵⁄₆, change ÷ to ×, flip ²⁄₃ to ³⁄₂: ⁵⁄₆ × ³⁄₂. Cancel: 6 and 3 share a factor of 3 → ⁵⁄₂ × ¹⁄₂. Multiply: 5 × 1 = 5, 2 × 2 = 4. Answer: ⁵⁄₄ = 1¼.

Mixed numbers — convert first

Just as with addition, convert any mixed number to an improper fraction before multiplying or dividing. Then apply the rules above.

A common mistake is to multiply only the whole-number parts together and forget the fractional parts. Always convert fully to improper fractions first — it removes the ambiguity.
Nova
Try this one

In a sale, a television is reduced by 18% to £516.

(a) Work out the original price of the television. [2]

After the sale, the price is increased by 18% from the sale price.

(b) Explain why the price after the increase is not the same as the original price, and find the new price. [2]

Nova's hint:

Part (a) is a reverse percentage; part (b) explores why percentage changes are not symmetrical.

Ask yourself: 'What percentage of the original price is £516, and what do I divide by to reverse a percentage reduction?' Think about whether 18% of £516 is the same value as 18% of the original price.

Try to Solve it with Nova?