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Fractions · level 2

Multiplying and cancelling

Multiplying fractions is the easy case: straight across. The mental trick is cancelling any top against any bottom first, so you only ever multiply small numbers.

Worked example: 3/8 × 4/9

numerator12
denominator72
in lowest terms1/6

Step by step

  1. 1

    Multiply straight across

    3 × 4 = 12 over 8 × 9 = 72

    No common denominator is needed for multiplication.

  2. 2

    Cancel before you multiply when you can

    3/8 × 4/9

    Any factor shared by a top and a bottom can be divided out first — the numbers stay small.

  3. 3

    Reduce: both divide by 12

    12/72 = 1/6

3/8 × 4/9 = 0.167

The theory behind it

Intuition

Fractions are ratios in their most honest form. Crosswise addition avoids hunting for a common denominator; cancelling first keeps the numbers small.

Common pitfalls

  • ×Cancelling across an addition sign — you may only cancel across multiplication.
  • ×Forgetting to reduce, which hides an obvious answer.

In the interview

Share shifts, mix questions and 'two thirds of the remaining third' arithmetic.