Fractions, decimals and percentages: what children learn
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.
Supplemental equivalence practice for fractions, decimals and percents. This prepares for percent reasoning without covering all of 6.RP.A.3.c.
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°.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
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%).
How should I choose this game for my learner?
Supplemental equivalence practice for fractions, decimals and percents. This prepares for percent reasoning without covering all of 6.RP.A.3.c.
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).