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

Work out \ \( \dfrac{3}{4} + \dfrac{1}{6} \).

Give your answer as a fraction in its simplest form.

[3]

Nova's hint:

This uses the skill of adding fractions with different denominators.

Ask yourself: 'What is the lowest common multiple of the two denominators?' Try converting both fractions so they share the same denominator before adding the numerators. For example, \( \frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} \).

Try to Solve it with Nova?