Fractions, Decimals and Percentages

Three ways of writing one amount. Being able to move between them is what turns hard-looking questions into easy ones.

Grades 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 is easier for a different job. Fractions are best for exact thirds and sevenths. Decimals are best for calculating. Percentages are best for comparing and for anything involving money.

The six moves

There are three forms, so there are six conversions. Each is one 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. A child who knows these stops calculating and starts recognising, and that frees up all the thinking for the actual question.

  • 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

Exam questions love a list with all three forms in it. The method is always the same.

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

Turning 35% into 3.5, or 0.35 into 3.5%. Ask which answer is bigger and sanity check it: a percentage is always the larger looking number, because it counts hundredths rather than wholes. 35% is 0.35, never 3.5.

2. Reading the digits instead of converting

Writing 14 as 14% or 0.14. The digits of a fraction have nothing to do with the digits of its decimal. Divide, every time, until the common ones are memorised.

3. Comparing forms without converting

Deciding 23 is bigger than 70% by looking at them. It is not: two thirds is about 66.7%. Convert first, always. Guessing works often enough to feel safe and fails exactly when the marks matter.

Practice questions

Seven questions. One attempt each, and the explanation appears once the answer is in.

Check yourself

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For parents

Make nine flashcards, one per row of the table, with all three forms on the back. Five minutes twice a week. Once your child recognises rather than calculates, percentage questions stop feeling like a topic and start feeling like reading, and the time saved goes into the part of the question that actually carries the marks.

What to learn next

What are percentages?Math · Grades 5 to 7Fractions to decimalsMath · Grades 5 to 7Percentage of a numberMath · Grades 5 to 7Comparing fractionsMath · Grades 4 to 6

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