Functional Skills Maths · England

Fractions, decimals and percentages

Switch confidently between fractions, decimals and percentages, put them in order, and work out a fraction or percentage of any amount — with and without a calculator.

Audience
Adults & apprentices
Levels
Level 1 · Level 2
Worked examples
4
Format
Print (A4/Letter) + answers

Learn

Three ways of writing the same amount

A fraction, a decimal and a percentage can all describe the same part of a whole. One half is 1/2, 0.5 and 50%. Functional Skills questions often mix the forms on purpose: a shop advertises a third off, a contract is 0.6 of full time, a survey reports 35%. Your job is usually to turn them into one form so you can compare or calculate.

It is worth knowing a handful of equivalents by heart, because they come up constantly and save time in the non-calculator section: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%, and 1/3 ≈ 0.333 ≈ 33.3%.

Converting between the forms

Fraction to decimal: divide the top number by the bottom number. 3/8 means 3 ÷ 8, which is 0.375. Decimal to percentage: multiply by 100, so 0.375 becomes 37.5%. Percentage to decimal: divide by 100, so 6% is 0.06 — note the zero, a common slip is writing 0.6.

Percentage to fraction: write the number over 100 and simplify. 35% is 35/100, and dividing top and bottom by 5 gives 7/20. Decimal to fraction works by place value: 0.65 is 65 hundredths, 65/100, which simplifies to 13/20.

Ordering mixed values

To put fractions, decimals and percentages in order, convert everything to decimals (or everything to percentages) and then compare. Line the decimals up with the same number of places: 0.6 is the same as 0.600, which makes it easy to see that it is smaller than 0.625. Always finish by writing the values in their original form, because that is what the question asked for.

Fractions and percentages of amounts

To find a fraction of an amount, divide by the bottom number and multiply by the top number. For 3/5 of £45, find one fifth (45 ÷ 5 = 9) and then three fifths (9 × 3 = 27), so the answer is £27.

Without a calculator, build percentages from easy pieces. 10% is the amount divided by 10, 5% is half of 10%, and 1% is the amount divided by 100. So 35% is 10% + 10% + 10% + 5%. With a calculator, multiply by the decimal: 17.5% of £260 is 0.175 × 260 = £45.50.

To write one amount as a percentage of another, make a fraction and multiply by 100. If you answered 18 questions correctly out of 24, that is 18 ÷ 24 × 100 = 75%. At Level 1 you will mostly work with familiar fractions and percentages; Level 2 questions use less friendly numbers, ask you to express one quantity as a percentage of another, and often combine several steps.

Worked example 1

Level 1: A jacket costs £64. In a sale it has 3/8 off. How much money is taken off?

  1. Find one eighth: £64 ÷ 8 = £8.
  2. Three eighths is 3 × £8 = £24.

Answer: £24.00 is taken off.

Worked example 2

Level 1: Put these in order, smallest first: 0.47, 2/5, 42%, 9/20.

  1. Change everything to decimals: 0.47; 2/5 = 2 ÷ 5 = 0.4; 42% = 0.42; 9/20 = 9 ÷ 20 = 0.45.
  2. Compare: 0.40, 0.42, 0.45, 0.47.
  3. Write them back in their original form.

Answer: 2/5, 42%, 9/20, 0.47 (smallest is 2/5 = 0.4)

Worked example 3

Level 2: Without a calculator, find 35% of £180.

  1. 10% of £180 = £18.
  2. 30% = 3 × £18 = £54.
  3. 5% = half of 10% = £9.
  4. 35% = £54 + £9 = £63.

Answer: £63.00

Worked example 4

Level 2: Amira scored 42 out of 56 on a test. What percentage is that?

  1. Write it as a fraction: 42/56.
  2. Divide: 42 ÷ 56 = 0.75.
  3. Multiply by 100: 0.75 × 100 = 75%.

Answer: 75%

Watch out

Common mistakes

  • Writing small percentages as the wrong decimal: 6% is 0.06, not 0.6.
  • Dividing by the top number instead of the bottom when finding a fraction of an amount — for 3/5 of £45, divide by 5, not 3.
  • Comparing fractions by looking only at the bottom numbers. A bigger denominator means smaller pieces, but you need the numerator too; convert to decimals to be sure.
  • Leaving an ordered list in decimals when the question gave fractions and percentages. Write the answer in the original form.

Real life

Where you'll use this at work or home

  • Shopping: comparing “a third off” with “30% off” to see which saves more.
  • Work: part-time contracts are often written as a decimal of full time, such as 0.8, and pay is worked out from that.
  • Recipes and DIY: using three quarters of a bag of compost or two thirds of a tin of paint.
  • Reading reports: test results, survey findings and targets are usually given as percentages.

Try it

Practice sheet

Functional Skills Maths · Level 1

Fractions, decimals and percentages

NameDate

Show your working. Give money to the nearest penny and include units in every answer.

  1. 1.A recipe uses 3/4 of a 500 g bag of flour. How many grams is that?
  2. 2.Write 0.35 as a percentage.
  3. 3.2/5 of the 30 staff at a care home work part-time. How many staff is that?
  4. 4.A restaurant bill is £86. You leave a 10% tip. How much is the tip?
  5. 5.A train fare is £48. A railcard saves 1/3. How much do you save?
  6. 6.Put these in order, largest first: 0.7, 3/4, 72%.
  7. 7.Dan earns £420 a week and saves 25% of it. How much does he save?
  8. 8.A 5 litre tin of paint is 0.6 used. How many litres have been used?
  9. 9.Write 3/5 as a decimal and as a percentage.
  10. 10.A 2 m length of skirting board has 15% cut off. How many centimetres are cut off?
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Questions

Frequently asked questions

Knowing the common ones (halves, quarters, fifths, tenths and thirds) saves a lot of time, especially in the non-calculator section. Others you can work out by division.

Decimals are usually easiest. Give them all the same number of decimal places, then compare digit by digit from the left.

Build it: 10% + 5% + 2.5%. Find 10%, halve it for 5%, then halve again for 2.5%, and add the three together.

Yes. Level 1 focuses on common equivalents and simple fractions or percentages of amounts; Level 2 uses harder numbers and multi-step problems. Check your awarding body's specification for the exact detail.

Next steps

Percentage change, VAT and discountsIncreases, decreases, discounts, VAT and reverse percentages.Ratio and proportionSharing in a ratio, recipes, best buys and inverse proportion.Money, interest and budgetingBudgets, simple and compound interest, and income tax.All Functional Skills Maths topicsThe full learning path, Level 1 and Level 2.

Last reviewed: 9 October 2026

Editor: Paul Smeaton CMgr FCMI