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Fractions · level 1

Adding fractions crosswise

You never need to hunt for a lowest common denominator. Multiply crosswise upwards for the top, multiply the bottoms for the bottom, then reduce once at the end.

Worked example: 2/3 + 1/4

numerator11
denominator12
in lowest terms11/12

Step by step

  1. 1

    Multiply crosswise, upwards

    2 × 4 = 8 and 1 × 3 = 3

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

  2. 2

    Add the two cross-products

    8 + 3 = 11

  3. 3

    Multiply the denominators

    3 × 4 = 12

  4. 4

    Already in lowest terms

    11/12 = 11/12

2/3 + 1/4 = 0.917

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.