Fractions, Decimals and Percentages

Three ways of writing one amount. Moving between them freely is what turns a question that looks hard into one a child can see the answer to, which is why this topic is worth more than its share of lesson time.

Decimals and percentages · topic 7 of 7Grades 5 to 7Number8 min read7 practice questions

One amount, three names

A fraction, a decimal and a percentage can all describe exactly the same amount.

12fraction0.5decimal=50%percentage=
Half of something, written three ways. Nothing changes between the boxes except the notation.
14fraction0.25decimal=25%percentage=
And a quarter, the same three ways. The form you use depends on the question, not on the amount.

Each form earns its keep on a different kind of job. Fractions handle exact thirds and sevenths without rounding anything away, decimals are what you want when there is arithmetic to do, and percentages are easiest to compare and are the language money is discussed in.

The six moves

Three forms means six possible conversions, which sounds like a lot until you see that each one is a single short step.

Between decimals and percentages

Decimal to percentage: multiply by 100. 0.35 becomes 35%.

Percentage to decimal: divide by 100. 35% becomes 0.35.

Both just move the digits two columns, because percent means per hundred.

Between fractions and the other two

Fraction to decimal: divide the top by the bottom. 34 is 3 ÷ 4 = 0.75.

Decimal to fraction: the last column names the denominator. 0.35 is 35100, which simplifies to 720.

Fraction to percentage: go through the decimal, or make the denominator 100.

Percentage to fraction: put it over 100 and simplify.

The decimal is the hub

If a conversion feels awkward, go via the decimal. Fraction to decimal to percentage is two easy steps instead of one hard one, and it works for every fraction, including the ones that never divide neatly.

The table to memorise

Nine rows, and they repay learning by heart more than anything else on this page. A child who recognises these rather than calculating them has their whole attention available for whatever the question is actually about.

  • 12 is 0.5 is 50%
  • 14 is 0.25 is 25%
  • 34 is 0.75 is 75%
  • 15 is 0.2 is 20%
  • 25 is 0.4 is 40%
  • 110 is 0.1 is 10%
  • 310 is 0.3 is 30%
  • 18 is 0.125 is 12.5%
  • 13 is about 0.333 is about 33.3%

Ordering a mixed list

Examiners are fond of a list with all three forms mixed into it, precisely because it catches children who can convert in one direction only. The method never changes.

Convert everything to one form, then order

Percentages are usually easiest, because they are all whole numbers out of 100 and there is no padding to worry about.

Order them, then write the answer back in the forms the question used.

Worked examples

1

Fraction to percentage

Write 38 as a percentage.
  1. Go via the decimal. Divide the top by the bottom: 3 ÷ 8 = 0.375.
  2. Now multiply by 100 to get a percentage.
  3. 0.375 × 100 = 37.5, so the answer is 37.5%.
  4. Sense check: 38 is a little under a half, and 37.5% is a little under 50%.
38 = 0.375 = 37.5%
2

Percentage to fraction

Write 60% as a fraction in its simplest form.
  1. Percent means per hundred, so start with 60100.
  2. Both numbers divide by 20, which is the highest common factor.
  3. 60 ÷ 20 = 3 and 100 ÷ 20 = 5.
  4. Finished check: 3 and 5 share no factor except 1.
60% = 35
3

Ordering a mixed list

Order these smallest first: 0.6, 55%, 12, 710
  1. Turn everything into percentages, since one of them already is.
  2. 0.6 becomes 60%. The half becomes 50%. 710 becomes 70%.
  3. Now order the numbers: 50, 55, 60, 70.
  4. Write them back in their original forms, in that order.
12, then 55%, then 0.6, then 710

Common mistakes

1. Moving the point the wrong way

35% becomes 3.5, or 0.35 becomes 3.5%, because the digits are moving and it is easy to lose track of which way. There is a quick sanity check: a percentage always looks like the bigger of the two numbers, since it counts hundredths where the decimal counts wholes. So 35% is 0.35, never 3.5.

2. Reading the digits instead of converting

14 gets written as 14% or 0.14, reading the digits straight off. The digits in a fraction have no relationship at all to the digits in its decimal, and the only cure while the common ones are still being learned is to actually divide, every single time, however obvious it looks.

3. Comparing forms without converting

23 gets judged bigger than 70% on sight. It is not, since two thirds is about 66.7%, and the two are close enough that no amount of staring will settle it. Guessing on questions like this works often enough to feel like a reliable skill and then fails on precisely the ones where the marks are.

Practice questions

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For parents

Make nine flashcards, one for each row of the table, with all three forms written on the back. Five minutes twice a week is plenty. Somewhere in the second or third week your child will stop working these out and start simply recognising them, and from that point percentage questions begin to feel more like reading than like calculating. The attention that used to go on the conversion goes into the part of the question that actually carries the marks.

Keep going

Maths CheckTwelve questions, five minutes, then a printable report naming what to work on next. Free, no sign up.OpenShow me the workingLong division, long multiplication and column methods, walked step by step on your own numbers.Open

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