Division, fractions and approximation under time pressure Exit
Speed maths

Division, fractions and approximation under time pressure

Division is where time goes. Divide by 5, 25 and 125 by multiplying instead, compare fractions without dividing, and approximate when the options are far apart.

Start with this

Most students lose time dividing. Dividing by 25 is harder than multiplying by 4, so do the multiplication instead.

Simplification and approximation questions ('approximately what value should replace ?') appear in most placement tests and bank-style papers. They reward three habits: turning division into multiplication, comparing fractions without long division, and rounding when the options allow it.

Divide by 5, 25 and 125 by multiplying

5 = 10/2, so dividing by 5 is the same as multiplying by 2 and dividing by 10. 25 = 100/4 and 125 = 1000/8 work the same way.

Dividing by 10, 100 or 1000 only moves the decimal point, so all the real work is a doubling or a × 4 or a × 8.

Worked example

4,375 / 125

  1. 4375 × 8 = 35,000.
    Why: 125 × 8 = 1000.
  2. 35000 / 1000 = 35.

Answer: 35

Compare fractions without dividing

To compare a/b with c/d, cross-multiply: compare a × d with b × c. Whichever side has the bigger product has the bigger fraction.

For several fractions, convert to percentages with the fraction table, or compare how far each is from 1 (1 - a/b).

Worked example

Which is bigger: 13/17 or 16/21?

  1. 13 × 21 = 273 and 17 × 16 = 272.
    Why: Cross products.
  2. 273 > 272, so 13/17 is bigger (only just).

Answer: 13/17

BODMAS without mistakes

Order: Brackets, then 'of', then Division and Multiplication from left to right, then Addition and Subtraction from left to right.

Division does NOT come before multiplication. They share one level and you go left to right. 12 / 3 × 2 = 4 × 2 = 8, not 12 / 6 = 2.

Worked example

Simplify 48 / 4 × 3 + 5 - 2 × 6

  1. 48 / 4 = 12, then 12 × 3 = 36.
    Why: Division and multiplication left to right.
  2. 2 × 6 = 12.
  3. 36 + 5 - 12 = 29.

Answer: 29

Approximation: when the options let you round

If the answer options are more than about 10% apart, you do not need the exact value. Round every number to the nearest friendly value, compute, and pick the nearest option.

Round in opposite directions when you can (one up, one down) so the errors cancel.

Worked example

Approximately: 399.8 × 24.9 / 50.1 = ? (a) 150 (b) 200 (c) 250 (d) 300

  1. 400 × 25 / 50.
    Why: Friendly numbers.
  2. = 200.

Answer: 200

Exam-hall time plan

Give each question at most 90 seconds on the first pass. If you are not near the answer by then, mark it and move on.

Look at the options before calculating: the unit digit, the size or the form of the answer often rules out two of them.

Do the easy topics of your paper first (percentages, averages, series), then return to the long ones (DI, puzzles).

Exam-hall time plan: reference

SituationWhat to do
Options far apartApproximate
Options close togetherCompute exactly, check the unit digit
'Find the number' typeTry the options from the middle
No starting value givenTake 100 or the LCM
Stuck after 90 sMark, skip, come back

Common mistakes

Doing all divisions before multiplications (12 / 3 × 2 = 2).
Same level, left to right: 12 / 3 = 4, then x 2 = 8.
Computing exactly when the options are 50 apart.
Round and move on; save the time for harder questions.

Your turn medium

Arrange 3/5, 5/8, 4/7 in increasing order.

  1. As percentages: 3/5 = 60%, 5/8 = 62.5%, 4/7 = 57.1%.
    Why: Converting to % is quick when you know the table.
  2. 4/7 < 3/5 < 5/8.

Answer: 4/7, 3/5, 5/8

Your turn medium

Simplify: 18 + 6 / 3 × 2 - 4

  1. Division and multiplication left to right: 6 / 3 = 2, then 2 × 2 = 4.
    Why: BODMAS: D and M before A and S, in reading order.
  2. 18 + 4 - 4 = 18.

Answer: 18

Your turn medium

Approximately what is 49.98% of 801.2 + 24.9% of 399.7? (a) 480 (b) 500 (c) 520 (d) 560

  1. 50% of 800 = 400 and 25% of 400 = 100.
    Why: The options are 20 apart, so rounding is safe.
  2. 400 + 100 = 500.

Answer: 500

Your turn medium

What is 3/7 as a decimal, to 6 places?

  1. 1/7 = 0.142857 repeating.
    Why: Sevenths all use the same cycle 142857.
  2. 3/7 starts at the 4: 0.428571.

Answer: 0.428571

Recap

Now practise

9 questions with full solutions.

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