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Fractions · level 1

Subtracting fractions crosswise

Subtraction uses the identical crosswise pattern — the only change is a minus sign between the two cross-products. Keep the order: first fraction's numerator leads.

Worked example: 5/6 − 1/4

numerator14
denominator24
in lowest terms7/12

Step by step

  1. 1

    Multiply crosswise, upwards

    5 × 4 = 20 and 1 × 6 = 6

    Each cross-product is the numerator rewritten over the common denominator.

  2. 2

    Subtract the second from the first

    20 − 6 = 14

  3. 3

    Multiply the denominators

    6 × 4 = 24

  4. 4

    Reduce: both divide by 2

    14/24 = 7/12

5/6 − 1/4 = 0.583

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.