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Fractions · level 2

Dividing by a fraction

Flip the second fraction and multiply. Dividing by 2/5 is multiplying by 5/2 — dividing by a number smaller than one makes the answer bigger, which is the sanity check to keep in mind.

Worked example: 3/4 ÷ 2/5

numerator15
denominator8
in lowest terms15/8

Step by step

  1. 1

    Turn the second fraction upside down

    3/4 ÷ 2/5 = 3/4 × 5/2

    Dividing by a fraction is multiplying by its reciprocal.

  2. 2

    Multiply straight across

    3 × 5 = 15 over 4 × 2 = 8

  3. 3

    Already in lowest terms

    15/8 = 15/8

3/4 ÷ 2/5 = 1.875

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.