Speed calculation · lesson 24 of 25 · free

Fractions × and ÷: cancel first — Speed Calculation

Multiplying fractions and then simplifying a big answer is slow. Cancel first: any top number and any bottom number that share a factor can both be divided by it. The numbers stay tiny and the answer comes out already in lowest terms. To divide, flip the second fraction and multiply.

The fast method

Cancel first — “divide a top and a bottom by the same number before multiplying”

  1. Dividing? Flip the second fraction and multiply: ÷ 2/3 is × 3/2.
  2. Cancel: a top and a bottom that share a factor — divide both by it.
  3. Multiply what is left: tops × tops, bottoms × bottoms. A bottom of 1 means a whole number.

Use it for: Recipes and sharing (half of 3/4 of a cake), fractions in Class 6–8, and olympiad speed rounds.

Worked example: 4/9 × 3/8 = 1/6

  1. 4 and 8 share 4: 4 → 1, 8 → 2.
  2. 3 and 9 share 3: 3 → 1, 9 → 3.
  3. 1/3 × 1/2 = 1/6.

Check: 4 × 3 = 12 and 9 × 8 = 72; 12/72 = 1/6 ✓

✏️ Practice

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🏁 Lesson 24 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass — and beat the clock: finish within 4 min.

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🖨️ Multiplying and Dividing Fractions Worksheet

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