Fractions, decimals and percentages: what children learn
Fractions, decimals and percentages are three different ways of writing the same proportion. ½, 0.5 and 50% all mean exactly the same amount. Year 6 pupils should recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
In this matching game, children pair cards that show the same value in different forms: a fraction with a percentage, a decimal with a percentage, or a fraction with a decimal. The cards cover halves, quarters, fifths, tenths, eighths (including ⅜ = 0.375 from the curriculum), twentieths, twenty-fifths, fiftieths and hundredths.
This topic covers the Year 6 statutory requirement in the National Curriculum in England (Number – fractions (including decimals and percentages)): pupils should be taught to “recall and use equivalences between simple fractions, decimals and percentages, including in different contexts”. Year 6 pupils are usually aged 10–11.
For families following US standards, the closest Common Core standard is 6.RP.A.3.c, which is taught in Grade 6.
How to play
Pick a card on the left, then the card on the right that matches it. Each game has 6 pairs. Wrong matches are counted as mistakes, and you get three stars for a game with no mistakes.
Step by step
- Percent means 'out of 100'. 25% means 25 out of 100, which is 25/100. That simplifies to ¼.
- Decimal to percentage: multiply by 100. 0.4 × 100 = 40, so 0.4 = 40%. Think of 0.4 as 0.40, which is 40 hundredths.
- Fraction to decimal: divide. A fraction is a division. ⅜ = 3 ÷ 8 = 0.375. For fifths, it is easier to make hundredths: ⅕ = 20/100 = 0.2.
- Learn the key families. ½ = 0.5 = 50%. ¼ = 0.25 = 25%. ¾ = 0.75 = 75%. ⅕ = 0.2 = 20%. ⅒ = 0.1 = 10%. ⅛ = 0.125 = 12.5%.
Worked examples
Example 1: Match 3/5 with a percentage.
Working: Multiply top and bottom by 20: 3/5 = 60/100.
Answer: 60%
Example 2: Match 0.05 with a percentage.
Working: 0.05 is 5 hundredths.
Answer: 5%
Example 3: Match 3/8 with a decimal.
Working: ⅛ = 0.125, so ⅜ = 3 × 0.125. Or work out 3 ÷ 8 using short division.
Answer: 0.375
Common mistakes and how to fix them
- Thinking 0.4 = 4%. Write 0.4 as 0.40: that is 40 hundredths, so 40%.
- Thinking ⅕ = 0.5 because of the 5. ⅕ means one whole split into 5 parts: 1 ÷ 5 = 0.2.
- Thinking 1/100 = 0.1. 0.1 is one tenth. One hundredth is 0.01, which is 1%.
Activities to try at home
- Spot percentages in shop sales: is '25% off' the same as 'a quarter off'?
- Look at battery or download percentages: what fraction is 75%?
- Make a set of matching cards (½, 0.5, 50%) and play pairs.
Ideas for the classroom
- Use a 10 × 10 grid: shade an amount and write it as a fraction, decimal and percentage.
- Order a mixed set such as ⅗, 0.55, 58% and ½ by converting them to the same form.
- Link to pie charts: 25% of a pie chart is a quarter of the circle, or 90°.
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
How do you turn a fraction into a percentage?
Make the denominator 100 if you can (3/20 = 15/100 = 15%). Otherwise divide to get a decimal, then multiply by 100 (⅛ = 0.125 = 12.5%).
Which equivalences should Year 6 pupils know by heart?
Halves, quarters, fifths and tenths are expected by Year 5 and Year 6. Eighths (such as ⅜ = 0.375) appear in the Year 6 programme of study as well.
What is the US equivalent?
Common Core 6.RP.A.3.c (Grade 6) covers percent as a rate per 100. Decimal notation for tenths and hundredths is 4.NF.C.6 (Grade 4).