Convert to multiplication
Dividing is slow; multiplying by a reciprocal is fast. Memorise:
- 1/7 ≈ 0.143
- 1/9 ≈ 0.111
- 1/11 ≈ 0.0909
- 1/12 ≈ 0.0833
- 1/13 ≈ 0.0769
340 / 7 ≈ 340 times 0.143 ≈ 48.6.
Factor the divisor
Break it into successive easy divisions.
456 / 24 = 456 / 8 / 3 = 57 / 3 = 19.
1260 / 36 = 1260 / 4 / 9 = 315 / 9 = 35.
Almost always faster than long division, and less error-prone.
Estimate first, refine if needed
Decide the precision the question requires before computing. On a multiple-choice screen with well-separated options, two significant figures is usually plenty and pursuing more wastes the clock.
Bracket the answer: 7834 / 41 is between 7834/40 = 195.85 and 7834/42, so roughly 191. If the options are 150, 190 and 230, you are already done.
Scaling to round numbers
Adjust both numbers to something convenient.
638 / 22: multiply both by 5 to get 3190 / 110 = 29.
Or simplify first: 638/22 = 319/11 = 29.
Common ratio shortcuts
Recognising a ratio directly beats computing it:
- Anything /25 is times 4 /100.
- Anything /50 is times 2 /100.
- Anything /125 is times 8 /1000.
450 / 25 = 1800/100 = 18.
Where this matters
Division shows up constantly in percentage and ratio questions on timed screens, and it is where most candidates lose time. See estimation for the order-of-magnitude version, and drill in mental math.