Year 6 maths · Key Stage 2 · Number – fractions (including decimals and percentages)

Year 6 fractions: simplifying, comparing, adding and multiplying

Year 6 brings together everything children know about fractions and adds new calculations. They simplify fractions using common factors, compare and order fractions including those greater than 1, add and subtract with different denominators and mixed numbers, multiply two simple fractions, and divide a fraction by a whole number. The key idea throughout is equivalent fractions: rewrite the fractions so the pieces are the same size, then calculate.

Simplifying and calculating with fractions, explained

Simplifying a fraction means writing it with the smallest whole numbers possible. Children find a common factor of the numerator and denominator and divide both by it. 18/24 can be divided by 6 to give 3/4, which is its simplest form because 3 and 4 share no factor other than 1. Children often do it in steps (18/24 to 9/12 to 3/4) before spotting the biggest factor straight away. Always dividing both numbers by the same number keeps the value the same.

To compare, order, add or subtract fractions with different denominators, children first rewrite them so the denominators match. The common denominator is found using common multiples: for thirds and quarters, 12 works because both 3 and 4 go into it. So 2/3 becomes 8/12 and 3/4 becomes 9/12, which shows 3/4 is the larger. Fractions greater than 1 are compared as mixed numbers or improper fractions, whichever is easier. Does 7/4 beat 1 3/5? Written as 1 3/4 and 1 3/5, both have 1 whole, and 3 quarters is more than 3 fifths because quarters are bigger pieces, so 7/4 is larger.

Adding and subtracting starts with the easier case, where one denominator is a multiple of the other: 1/2 + 1/8 = 4/8 + 1/8 = 5/8. Later cases need both fractions changed, as in the worked example below. With mixed numbers, children can add the whole numbers and the fractions separately, or turn everything into improper fractions first. Either way, the answer should be simplified and any improper fraction written as a mixed number. For subtraction, they sometimes need to exchange one whole into parts.

Multiplying two simple proper fractions is more straightforward than adding them: multiply the numerators and multiply the denominators. 1/4 × 1/2 = 1/8, and 2/3 × 3/5 = 6/15 = 2/5. Children are taught to see why with a picture: half of a quarter is an eighth. Dividing a fraction by a whole number splits each part into smaller ones, so 1/3 ÷ 2 = 1/6: half of a third is a sixth. In the same way, 3/4 ÷ 3 = 1/4, because three quarters shared into three equal groups gives one quarter in each. Schools may also give problems that work backwards from a fraction, such as: a quarter of a length is 36 cm, so the whole is 36 × 4 = 144 cm.

Words your child will hear

Simplest form: A fraction written with the smallest possible numerator and denominator, such as 3/4 instead of 18/24.
Common denominator: A denominator that two or more fractions can be changed to share, such as 12 for thirds and quarters.
Proper fraction: A fraction less than 1, with the numerator smaller than the denominator, such as 3/5.
Improper fraction: A fraction of 1 or more, with the numerator at least as big as the denominator, such as 17/12.
Mixed number: A whole number and a fraction together, such as 4 5/12.
Equivalent fractions: Fractions with the same value, like 2/3 and 8/12.
Lowest common multiple: The smallest number that both denominators go into, often used as the common denominator. For 3 and 4 it is 12. Any common multiple works, but the lowest keeps the numbers small.

What the National Curriculum says

In Year 6, pupils should be taught to:

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
Compare and order fractions, including fractions > 1
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8]
Divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Work out 1 2/3 + 2 3/4. Give the answer as a mixed number in its simplest form.

The denominators are different, so find a common multiple. Multiples of 3 are 3, 6, 9, 12; multiples of 4 are 4, 8, 12. The lowest common multiple is 12, so use twelfths.
Change each fractional part to twelfths. For thirds, multiply the top and bottom by 4: 2/3 = 8/12. For quarters, multiply top and bottom by 3: 3/4 = 9/12.
2/3
8/12
3/4
9/12
Add the fractional parts: 8/12 + 9/12 = 17/12. This is more than one whole, so write it as a mixed number: 17/12 = 1 5/12.
Add the whole numbers: 1 + 2 = 3. Then add the 1 5/12 from the previous step: 3 + 1 5/12 = 4 5/12.
Check that it is in simplest form: 5 and 12 have no common factor other than 1, so 5/12 cannot be simplified. Check it is sensible: 1 2/3 is just under 2 and 2 3/4 is just under 3, so the total should be under 5. Both fractional parts are more than a half, so together they make more than 1 and the total is more than 4. 4 5/12 fits.

1 2/3 + 2 3/4 = 4 5/12

Common mistakes and how to help

Adding the numerators and the denominators: 1/2 + 1/8 = 2/10

Children copy the pattern from whole-number addition and add across the top and across the bottom.

What helps: Remind them that the denominator names the size of the pieces. Halves and eighths are different sizes, so change the halves to eighths first (4/8 + 1/8 = 5/8). A fraction bar shows it quickly.

Thinking that multiplying always makes a number bigger

With whole numbers, 3 × 4 is bigger than both 3 and 4, so 1/4 × 1/2 giving 1/8 feels wrong.

What helps: Read the multiplication as “of”: half of a quarter is an eighth, so the answer is smaller. Folding a paper strip into quarters and then folding one quarter in half shows it.

Subtracting the smaller fraction from the larger, however they sit: 3 1/4 − 1 3/4 = 2 2/4

The child takes 1 from 3 and 1/4 from 3/4, ignoring that 1/4 is smaller than 3/4, so the fractional part can’t be taken away directly.

What helps: Write both as improper fractions: 13/4 − 7/4 = 6/4 = 1 1/2. Or exchange one whole of the 3 into 4 quarters, making 2 and 5/4. A number line counting on from 1 3/4 to 3 1/4 also works.

Stopping simplification part-way, or simplifying only one number

6/15 is divided by 3 on the top only, or 12/18 is left at 6/9 because the child stops at the first common factor they see.

What helps: Ask “Can both numbers still be divided by something?” until the answer is no. Both must be divided by the same number every time. Listing the factors of the numerator and denominator finds the biggest at once.

How to help at home

Fold, cut and compare. Use paper strips to make thirds, quarters, sixths and twelfths. Laying them side by side lets your child see why 2/3 = 8/12, and which of two fractions is bigger, without a rule to remember.
Recipe fractions. Halve or share a recipe: “The recipe needs 3/4 of a bag of pasta, and we’re making half as much. How much now?” (Half of 3/4 is 3/8.) Real quantities make fractions of fractions easier to picture. Keep any cooking adult-supervised.
Work backwards from a part. Say “I’ve read 3/5 of this book and it was 90 pages. How long is the whole book?” Finding one part first (30 pages for 1/5) and then the whole (150 pages) is the way these problems are taught.
Which is bigger? Offer pairs such as 5/8 and 2/3, or 7/4 and 1 3/5, and ask your child to prove which is larger. The reasoning (common denominator, mixed numbers) matters more than the answer itself.
Simplify with a factor list. Pick a fraction like 28/42. Ask for the factors of 28 and 42, the biggest one they share (14) and the simplified result (2/3). It revisits factors and fractions together.

Updated 20 October 2026.