Professional and Subprofessional · Civil Service Exam

Fractions and decimals

Converting between fractions, decimals and percents, and adding, subtracting and multiplying fractions - all of it without a calculator.

There is no calculator, so the method taught at school is the wrong tool: long division is correct and too slow for an item worth about eleven seconds. What separates people here is a short list of equivalences known by sight - the halves, thirds, quarters, fifths, eighths and tenths - because those are the fractions that produce clean decimals, which is exactly why an item writer reaches for them.

For anything not on that list, go through a power of ten rather than dividing. If the denominator divides into 10, 100 or 1000, multiply top and bottom to get there and read the decimal off: 7/20 becomes 35/100 becomes 0.35, in one step. Going the other way, say the decimal aloud - `thirty-five hundredths` is where the denominator comes from.

Two rules decide most of the marks. Reduce before you look at the options, because an answer that is arithmetically right and not in lowest terms is marked wrong and the unreduced version is usually on offer. And cancel before multiplying rather than after, which keeps the numbers small enough to do in your head.

Worked examples

Try these, then read why.

Written for this platform and generated from the same bank the practice sets draw on. Every wrong option is explained, because knowing why a distractor was tempting is most of the learning.

Express 0.875 as a percent.

  1. A20%
  2. B75%
  3. C50%
  4. D87.5% (correct)

7/8 = 0.875 = 87.5%. A fraction becomes a decimal by dividing the top by the bottom, and a decimal becomes a percent by moving the point two places right. These few values are worth knowing by sight; they turn up inside percentage and word problems where working them out costs time you need elsewhere.

  • A This is the value of a different fraction in the same form.
  • B This is the value of a different fraction in the same form.
  • C This is the value of a different fraction in the same form.

What is 3/4 + 5/6, in lowest terms?

  1. A19/12 (correct)
  2. B38/24
  3. C13/8
  4. D4/5

Put both over 24: 18/24 + 20/24 = 38/24, which reduces to 19/12. The question asks for lowest terms, so an unreduced answer is only most of the way there.

  • B This is not the value of the expression in lowest terms.
  • C This is not the value of the expression in lowest terms.
  • D This adds the tops and the bottoms separately. Denominators are not added; they have to be made the same first.

What is 3/6 x 6/8, in lowest terms?

  1. A19/48
  2. B2/3
  3. C3/8 (correct)
  4. D18/48

Multiply across: 3 x 6 over 6 x 8 = 18/48, which reduces to 3/8. The question asks for lowest terms, so an unreduced answer is only most of the way there.

  • A This is not the value of the expression in lowest terms.
  • B This is not the value of the expression in lowest terms.
  • D This is not the value of the expression in lowest terms.

Practise this properly.

Three examples show you the format. Finding out whether fractions and decimals is actually costing you marks takes a measured set, which is what the free diagnostic is for.

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