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Making fraction calculations easier

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Fractions

Making fraction calculations easier

Four tricks that turn an awkward fraction calculation into one you can do in your head.

Turn it into a sum you can do in your head1/4 of 6004 = 2 × 2, so halve twice600 → 300 → 1503/5 of 120use 6/10 — ÷10 is easier12 × 6 = 727/8 of 400find 1/8 and subtract it400 − 50 = 350also: cancel common factors BEFORE multiplying, to keep the numbers small
Whichever trick you use, the order of operations still applies.

Trick 1 — break the fraction into factors

1/4 of 600. Since 4 = 2 × 2, finding a quarter is the same as halving twice: 600 ÷ 2 = 300 300 ÷ 2 = 150 So 1/4 of 600 = 150 — no long division needed.

Trick 2 — use an equivalent fraction

3/5 of 120. Dividing by 5 is fiddly; dividing by 10 is not. So change 3/5 into 6/10: 1/10 of 120 = 12 6/10 of 120 = 12 × 6 = 72 So 3/5 of 120 = 72.

Trick 3 — cancel before you multiply

When multiplying fractions, look for common factors in the numerator and denominator FIRST. (7 × 8)/(10 × 4) Replace 8 with 2 × 4, because there is already a 4 on the bottom: = (7 × 2 × 4)/(10 × 4) The 4s cancel: = (7 × 2)/10 = 14/10 = 7/5 Cancelling first keeps the numbers small.

Trick 4 — take the small fraction away

Instead of working out a LARGE fraction of a number, work out the small one and subtract. 7/8 of 400? Rather than seven eighths, find one eighth and take it off: 1/8 of 400 = 50 400 − 50 = 350 And remember: whichever trick you use, the correct ORDER OF OPERATIONS still applies.

Worked examples

1/4 of 600 by halving twice

  1. 4 = 2 × 2, so halve, then halve again.
  2. 600 ÷ 2 = 300.
  3. 300 ÷ 2 = 150.

Answer: 150

3/5 of 120 using tenths

  1. Change 3/5 into 6/10.
  2. 1/10 of 120 = 12.
  3. 6 × 12 = 72.

Answer: 72

(7 × 8)/(10 × 4) by cancelling first

  1. Write 8 as 2 × 4.
  2. The 4s cancel.
  3. (7 × 2)/10 = 14/10.

Answer: 7/5

7/8 of 400 by subtracting

  1. 1/8 of 400 = 50.
  2. 400 − 50 = 350.

Answer: 350

1/8 of 800 by halving three times

  1. 8 = 2 × 2 × 2.
  2. 800 → 400 → 200 → 100.

Answer: 100

Why cancel before multiplying?

  1. It keeps the numbers small.
  2. You would have to cancel afterwards anyway.

Answer: Same answer, easier arithmetic

Where you see this in real life

  • Finding 1/4 of a bill in your head by halving twice is faster and less error-prone than dividing by 4.
  • A 7/8-full tank: work out the 1/8 that is missing and subtract — usually far quicker.

Key words

Factor
a number that divides exactly into another
Equivalent fraction
a fraction of equal value written differently
Cancel
divide top and bottom by a common factor
Simplest form
written with the smallest possible numbers
Halving
dividing by 2
Order of operations
brackets, then × and ÷, then + and −
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