How to help your child with fractions
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Almost everything in primary fractions rests on two ideas. A fraction is a number of equal parts of a whole. And you can change how a fraction is written without changing its size. When those two ideas are secure, the methods stop looking like tricks.
This guide follows roughly the order used in English primary schools: halves and quarters in Key Stage 1, equivalent fractions and fractions of amounts in lower Key Stage 2, and adding fractions with different denominators in Year 6. Find the step your child is on and start a little before it.
Numerator and denominator
- The denominator (bottom number) says how many equal parts the whole is split into.
- The numerator (top number) says how many of those parts you have.
So 3/5 means "five equal parts, and we have three of them". A handy memory aid: the denominator is the down number, and it names the size of the pieces.
The word equal matters. A rectangle cut into four pieces of different sizes is not cut into quarters. Fold one paper strip into four equal parts, cut another into four pieces by eye, and ask your child which one shows quarters.
Draw a bar
Most schools now use a long rectangle, the bar model, rather than a pizza. Bars are easier to draw accurately and easier to compare. When your child is stuck on any fraction question, drawing a bar is a good first move.
Fractions of amounts
The rule is "divide by the bottom, multiply by the top". The bar above is that rule in picture form.
3/4 of 20. 20 ÷ 4 = 5, so one quarter is 5. Three quarters is 5 × 3 = 15.
2/5 of 35. 35 ÷ 5 = 7, so one fifth is 7. Two fifths is 7 × 2 = 14.
A child who forgets the rule but can draw the bar will still get there.
Two word problems
"There are 30 children in a class. 2/5 of them walk to school. How many do not walk?" One fifth of 30 is 6, so 12 walk. The question asks about the others: 30 − 12 = 18. Many children stop at 12. Drawing the bar, with 2 of 5 boxes shaded, makes the unshaded 3 boxes (3 × 6 = 18) hard to miss.
"3/4 of a number is 18. What is the number?" This one runs backwards, and a bar is the easiest way in. Draw a bar of 4 boxes and shade 3; those 3 boxes total 18, so each box is 18 ÷ 3 = 6. The whole bar is 4 × 6 = 24. Check: 3/4 of 24 is 18.
Equivalent fractions
1/2, 2/4, 3/6 and 50/100 are all the same amount written in different ways. You can multiply or divide the top and bottom by the same number and the size stays the same.
Write 3/4 with a denominator of 20. 4 × 5 = 20, so multiply the top by 5 too: 3 × 5 = 15. So 3/4 = 15/20.
Simplify 12/18. The largest number that divides into both is 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12/18 = 2/3.
If your child divides by 2 first and gets 6/9, that is fine. They just keep going until nothing else divides into both numbers. Quick times tables make this much easier, which is why our weekly times tables plan pairs well with fractions work.
Comparing fractions
Same denominator: 5/8 is bigger than 3/8, because you have more pieces of the same size.
Numerator of 1: here children are often surprised. 1/8 is smaller than 1/4, because the whole has been cut into more pieces. Share a cake between eight people instead of four and the point makes itself.
Anything else: rewrite both fractions with a common denominator.
Which is bigger, 2/3 or 3/5? Both 3 and 5 go into 15. 2/3 = 10/15 and 3/5 = 9/15, so 2/3 is bigger.
Adding and subtracting
With the same denominator, add the numerators and keep the denominator: 2/7 + 3/7 = 5/7. You are counting sevenths.
With different denominators, make them the same first. This is Year 6 work.
1/3 + 1/4. A common denominator is 12. 1/3 = 4/12 and 1/4 = 3/12, so the total is 7/12.
1/2 + 1/5. A common denominator is 10. 5/10 + 2/10 = 7/10.
Mixed numbers and improper fractions
An improper fraction has a numerator at least as big as its denominator, such as 11/4. A mixed number has a whole-number part, such as 2¾. To convert 11/4, ask how many whole fours fit into 11: two, making 8, with 3 left over. So 11/4 = 2¾.
Multiplying and dividing (Years 5 and 6)
- Fraction × whole number is repeated addition: 3 × 2/5 = 6/5 = 1⅕.
- Fraction × fraction: multiply the tops and multiply the bottoms. 2/3 × 3/5 = 6/15 = 2/5.
- Fraction ÷ whole number: 1/2 ÷ 3 means sharing a half into three equal parts. Each part is 1/6. Draw a bar, halve it and split the half into three.
Mistakes worth watching for
Adding the bottoms. 1/2 + 1/3 = 2/5 is the classic error. Ask whether 2/5 is more or less than 1/2. It is less, which cannot be right after adding something on. That kind of sense check catches many fraction slips.
"A bigger denominator means a bigger fraction." Go back to the cake or the paper strips.
Wobbly drawings. Circles cut into uneven slices give wrong answers. Bars on squared paper avoid this.
Changing only the bottom. 3/4 does not become 3/20. Whatever happens to the denominator must happen to the numerator.
Not simplifying. 6/15 is not wrong, but many questions ask for the simplest form, so build the habit of asking "Can this be simplified?"
Seven questions to try
- Shade 3/8 of a bar split into 8 equal parts.
- Write 2/3 as a fraction with denominator 12.
- Simplify 15/25.
- Find 3/5 of 40.
- Which is bigger, 3/4 or 5/8?
- Work out 1/2 + 1/5.
- Write 13/5 as a mixed number.
Answers: 1) 3 of the 8 parts shaded 2) 8/12 3) 3/5 4) 24 5) 3/4, because 3/4 = 6/8 6) 7/10 7) 2⅗
For more practice, the EduPrintables worksheet library has printable sheets that suit ten-minute sessions, and ModernScholar's maths activities are free for children who prefer a screen.
Fractions, decimals and percentages
These are three ways of writing the same amount. A small set learned by heart pays off from Year 5 onwards, especially on the KS2 arithmetic paper.
| Fraction | Decimal | Percentage |
|---|---|---|
| 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% |
| 1/100 | 0.01 | 1% |
With these, 25% of 360 becomes "a quarter of 360", which is 90, and 0.75 of 40 becomes "three quarters of 40", which is 30.
If your child freezes as soon as a fraction appears, step back to paper strips, measuring jugs or sharing food, where the fraction has a real meaning. Our article on what to do when a child says "I'm bad at maths" has more on rebuilding confidence, and column methods for parents covers the written calculations fractions often lead into.
Sources and further reading
- National curriculum in England: mathematics programmes of study – the fractions objectives for each year group, from Year 1 halves to Year 6 division of fractions.
- Teaching for mastery (NCETM) – background on the approach behind bar models and the visual methods many schools use.
- National curriculum assessments: past test materials – KS2 papers with plenty of fraction questions in the real test format.
