Improve Tuition · Non-Calculator Maths · Year 5–9
Lesson · Practice · Steps

Multiplying & Dividing Fractions

Cancel down, switch between mixed and improper, then multiply and divide — all by hand.

20 questions · 4 sections · three interactive steppers · no time pressure

What's really happening

Fractions are friendly without a calculator if you keep two habits: always simplify at the end, and turn any mixed number into an improper fraction before you multiply or divide. Get those two right and the rest is just times tables.

1 · Cancelling down (simplifying)

Divide the top (numerator) and bottom (denominator) by the same number, again and again, until they share no common factor. Tap through it:

Cancelling downSimplify 24/36

2 · Mixed numbers ↔ improper fractions

A mixed number has a whole part and a fraction part; an improper fraction has a top bigger than its bottom. You must be able to swap between them.

423 = (4×3)+23 = 143 Mixed → improper: whole × bottom, add the top, keep the bottom.
234 = 23 ÷ 4 = 5 r 3 = 534 Improper → mixed: divide top by bottom — the whole is the answer, the remainder goes on top. (That's short division.)

3 · Multiplying fractions

Multiply the tops together and the bottoms together — then simplify. Tap through it:

Multiplying fractions2/3 × 6/7

4 · Dividing fractions

Keep the first, flip the second, change ÷ to × — “keep, flip, change”. With mixed numbers, convert first. Tap through it:

Dividing fractions · with mixed numbers1½ ÷ 2¼
RememberWhen multiplying or dividing mixed numbers, turn them into improper fractions first. And you only “flip” for division — never for multiplication.
Learning Objective 1 · Year 5–6
Section A · Simplifying
Cancel a fraction down to its simplest form.
Success criteria — I can:
Learning Objective 2 · Year 5–7
Section B · Mixed ↔ improper
Convert between mixed numbers and improper fractions.
Success criteria — I can:
Learning Objective 3 · Year 6–8
Section C · Multiplying
Multiply fractions and give the answer in its simplest form.
Success criteria — I can:
Learning Objective 4 · Year 6–9
Section D · Dividing
Divide fractions and mixed numbers using keep–flip–change.
Success criteria — I can:
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