Fractions, Decimals and Percentages Help: Why Your Child Keeps Getting Stuck (And What Actually Works)

Ask your child to write 0.5 as a percentage and the answer comes straight back. Then ask which is biggest out of 0.6, five eighths and 62%, and most children pick 62% because it has the biggest number in it.

I have been teaching this topic for years, to 11+ children and to GCSE students who still find it slippery at sixteen. The children who struggle usually know each conversion on its own. What they cannot do yet is see that the three forms are the same amount written three ways.

The real problem isn't the conversions

Most of the marks lost here come from three habits, and none of them is a gap in times tables.

Reading the digits instead of the value. A child sees 0.5 and writes 5%, or sees 0.05 and writes 50%. They have learned that the digits move two places, but not which way or why, so they guess. A decimal is a number of tenths and hundredths, and a percentage is a number of hundredths, and until that clicks the rule is a coin toss.

Treating a fraction as two numbers. Three fifths becomes 3.5, or one eighth becomes 0.8, because the child is writing the top and bottom next to each other with a point between them. A fraction is a division, three divided by five, and it gives one number.

Comparing without converting. Put 0.6, five eighths and 62% in front of a child and they compare the look of the numbers. The only reliable way is to write all three in the same form first, and then the order is obvious.

Why worksheets alone don't fix it

There are six routes between the three forms, fraction to decimal, decimal to fraction, and so on. A typical worksheet practises one route per page, so a child can get twenty questions right in a row by repeating one move without thinking about what the numbers mean.

The exam does the opposite. It mixes the forms inside a longer question, often about money, a survey or a class of pupils, and never says which route to take. A question might tell you that a quarter of a class walk to school, 0.3 cycle and 35% come by bus, then ask what percentage come by car. The child has to decide to turn everything into percentages, add 25, 30 and 35 to get 90, and see that 10% is left. Nothing on a one-route worksheet prepares them for that first decision.

The skills that trip children up, in order

Each of these leans on the one above it, so if your child is stuck on number 9, the fix is usually somewhere between 1 and 5.

1. Percent means out of 100. 37% is 37 hundredths. This one sentence is the key to every other skill on the list.

2. Decimals to percentages and back. Multiply or divide by 100, and know why the digits move two places. 0.07 is 7%, and 70% is 0.7.

3. Decimals to fractions. Read the decimal as tenths or hundredths, then simplify. 0.35 is 35 hundredths, which is 7/20.

4. Percentages to fractions. Put the percentage over 100 and simplify. 45% is 45/100, which is 9/20.

5. The key facts. Halves, quarters, fifths, tenths and eighths as decimals and percentages, known by heart, plus one third as 33⅓%.

6. Fractions to decimals using equivalent fractions. Make the denominator 10 or 100 where you can. 3/25 is 12/100, which is 0.12.

7. Fractions to decimals by dividing. When the denominator will not go into 100, divide. 3/8 is 0.375, and 2/3 is 0.666 with the 6 repeating forever, which is where rounding and recurring decimals come in.

8. Fractions to percentages. Convert to a decimal first, then to a percentage, so 3/8 becomes 0.375 and then 37.5%.

9. Ordering a mixed list. Convert every value to the same form, write them underneath each other, then compare.

10. Multi step questions. The walk, cycle and bus question above, where the amounts arrive in different forms and your child has to choose one form to work in.

What closes the gap

Three habits make the biggest difference, and none of them needs a worksheet.

Say every amount three ways. Whenever a fraction, a decimal or a percentage turns up, in a recipe, a phone battery, a sale sign, ask for the other two forms. It takes ten seconds and it builds the idea that they are one amount. Children who do this for a few weeks stop seeing three separate topics.

Convert before you compare. Teach one rule for every ordering question. Choose a form, usually percentages, write every value in that form in a column, then put them in order. For 0.6, five eighths and 62% the column reads 60%, 62.5% and 62%, and the order is 0.6, then 62%, then five eighths.

Learn a small set of facts and build from them. If your child knows that one eighth is 12.5%, then three eighths is three lots of 12.5%, which is 37.5%, with no division needed. A handful of facts known by heart does more than a long table stuck on the fridge.

The lessons we built to fix this

Our Fractions, Decimals and Percentages Mastery is two interactive lessons, 10 units and 180 questions, taught in the order of the list above.

Lesson 1, Decimals and Percentages, covers decimals to percentages and back, decimals and percentages to fractions, and the key facts. A hundred square names whatever your child shades as a fraction, a decimal and a percentage at once, so the three forms are one picture from the start.

Lesson 2, Fractions and Ordering, covers fractions to decimals by equivalents and by dividing, recurring decimals and rounding, fractions to percentages, ordering mixed lists and multi step problems. Short division is built one column per click, so a recurring decimal appears the way your child would write it on paper.

Every unit opens with worked examples your child clicks through one line at a time. The answers stay hidden until they click to check, and each question bank has a New Questions button when they want another set. The pair ends with three 20 question challenges where the questions are not labelled, so your child has to work out which conversion is being asked for, as in the exam.

These are lessons 36 and 37 of The Complete 11+ Maths Course, which sits them straight after percentages, so your child meets them in the order that makes each one easier.

What to do this week

Two questions will tell you where your child is.

First, ask them to write 0.3 as a percentage, then 3% as a decimal. The answers are 30% and 0.03. If they give 3% for the first, or 0.3 for the second, they are moving digits without knowing why, and skills 1 and 2 are where to start.

Then write 0.6, 5/8 and 62% on a piece of paper and ask for them in order, smallest first. The answer is 0.6, then 62%, then 5/8, because five eighths is 62.5%. If your child cannot say how they decided, teach the convert before you compare habit before anything else.

The free fractions, decimals and percentages practice page has twelve more questions at three levels, with the answers hidden until your child clicks, and it prints as a worksheet if you want one on paper.

When you want the topic taught properly from the first idea to the exam questions, the two lessons cover it end to end. If you would like a second opinion on where your child is, book a free consultation and we will talk it through.

Our guide to 11+ maths at home has a quick question for this topic and for the other 15 areas of 11+ maths.

Aadam, SHLC Tutors