Fractions Made Simple: A Parent's Complete Guide to KS2 Fractions

• Numerator (top) = how many parts you have; denominator (bottom) = total equal parts
• The golden rule: whatever you do to the numerator, do the same to the denominator
• To add fractions with different denominators: find a common denominator first
• Multiplying fractions: multiply tops together, multiply bottoms together — then simplify
• Dividing by a fraction: flip the second fraction and multiply (“Keep, Change, Flip”)
• ½ = 0.5 = 50% · ¼ = 0.25 = 25% · ¾ = 0.75 = 75% · 1⁄5 = 0.2 = 20%
• Fractions account for roughly 20–25% of the KS2 Maths SATs

Why Fractions Feel So Hard

Fractions are consistently one of the most challenging topics in primary school maths — for children and for parents trying to help at home. There are good reasons for this:

• Counter-intuitive behaviour: In whole-number arithmetic, bigger numbers mean “more.” With fractions, a bigger denominator means smaller pieces (1⁄8 is smaller than 1⁄3). This conflicts with early number sense
• Multiple representations: The same amount can be written as ½, 2⁄4, 4⁄8, 0.5, or 50%. Children need to recognise all forms as equivalent
• Different rules for different operations: Adding fractions requires common denominators, but multiplying fractions doesn't. The rules feel arbitrary unless the underlying concepts are understood
• Parents learned differently: Many adults were taught fractions procedurally (“just follow the rule”) without understanding why the rules work. The current curriculum emphasises conceptual understanding alongside procedural fluency

The good news: fractions follow consistent, logical rules. Once a child understands why each operation works the way it does, the procedures stop feeling random and become intuitive.

The Basics: Numerator and Denominator

Every fraction has two parts:

• The numerator (top number) — how many parts you have
• The denominator (bottom number) — how many equal parts the whole is divided into

So ¾ means: the whole is divided into 4 equal parts, and we have 3 of them.

A useful memory hook: denominator = down below.

Crucially, fractions only work when the parts are equal. Cutting a pizza into 4 uneven slices and eating 3 of them is not ¾ — the denominator tells us how many equal parts exist.

Equivalent Fractions

Equivalent fractions look different but represent the same amount. Understanding this is fundamental to almost every other fractions operation.

Examples: ½ = 2⁄4 = 3⁄6 = 4⁄8 = 5⁄10 = 50⁄100

To find an equivalent fraction, multiply (or divide) both the numerator and denominator by the same number:

• ½ → multiply both by 3 → 3⁄6 ✓
• 2⁄5 → multiply both by 4 → 8⁄20 ✓
• 6⁄9 → divide both by 3 → 2⁄3 ✓

Why this works: Multiplying both parts by the same number is the same as multiplying by 1 (e.g. 3⁄3 = 1). The fraction's value doesn't change — only its appearance does. This is worth explaining to children, because it turns the rule from “something you must remember” into “something that makes sense.”

Simplifying Fractions

Simplifying (or reducing) a fraction means dividing both the numerator and denominator by their highest common factor (HCF) to express the fraction in its simplest form.

Worked example: Simplify 12⁄18

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Highest common factor = 6
• 12 ÷ 6 = 2, 18 ÷ 6 = 3
• Answer: 2⁄3

Tip: If your child finds the HCF tricky, they can simplify in steps — divide by any common factor first, then repeat. 12⁄18 → ÷2 → 6⁄9 → ÷3 → 2⁄3. Same result, just two steps instead of one.

Comparing and Ordering Fractions

To compare fractions with the same denominator, simply compare the numerators: 5⁄8 > 3⁄8 because 5 > 3.

To compare fractions with different denominators, convert them to equivalent fractions with a common denominator:

Which is bigger: 2⁄3 or 3⁄5?

• Common denominator = 15
• 2⁄3 = 10⁄15
• 3⁄5 = 9⁄15
• 10⁄15 > 9⁄15, so 2⁄3 is bigger

Children also need to know benchmark fractions — common reference points like ½. Is 3⁄7 more or less than a half? Since half of 7 is 3.5, and 3 < 3.5, then 3⁄7 is less than ½. This kind of estimation is valuable and frequently tested.

Adding and Subtracting Fractions

Same denominator (straightforward)

When the denominators match, add or subtract the numerators. The denominator stays the same:

3⁄7 + 2⁄7 = 5⁄7 · 5⁄9 − 2⁄9 = 3⁄9 = 1⁄3

Different denominators

This is where most children need extra practice. The steps are:

1. Find a common denominator (often the lowest common multiple of the two denominators)
2. Convert both fractions to equivalent fractions with that denominator
3. Add or subtract the numerators
4. Simplify the result if possible

Worked example: 2⁄3 + 1⁄4

• LCM of 3 and 4 = 12
• 2⁄3 = 8⁄12 (multiply both by 4)
• 1⁄4 = 3⁄12 (multiply both by 3)
• 8⁄12 + 3⁄12 = 11⁄12

Worked example: 5⁄6 − 1⁄4

• LCM of 6 and 4 = 12
• 5⁄6 = 10⁄12 (multiply both by 2)
• 1⁄4 = 3⁄12 (multiply both by 3)
• 10⁄12 − 3⁄12 = 7⁄12

Tip: The most common error children make is adding the denominators as well as the numerators (e.g. 1⁄3 + 1⁄4 = 2⁄7). This is wrong because the denominator defines the size of the parts — you cannot add parts of different sizes without converting first. Using a visual (pizza slices, fraction bars) helps children see why.

Multiplying Fractions

Multiplying fractions is, surprisingly, the simplest fractions operation:

Multiply the numerators together. Multiply the denominators together. Simplify.

Worked example: 2⁄3 × 3⁄5

• Numerators: 2 × 3 = 6
• Denominators: 3 × 5 = 15
• Result: 6⁄15 = 2⁄5 (simplified by dividing both by 3)

Multiplying a fraction by a whole number:

3 × 2⁄5 = (3 × 2)⁄5 = 6⁄5 = 1 1⁄5 (one and one fifth)

Why does multiplying fractions give a smaller answer? Children are used to multiplication making numbers bigger. With fractions less than 1, multiplying gives a smaller result — because you're taking “a part of a part.” 1⁄2 × 1⁄2 = 1⁄4 makes sense: half of a half is a quarter.

Dividing Fractions

Dividing by a fraction uses the “Keep, Change, Flip” method (also known as “multiply by the reciprocal”):

1. Keep the first fraction as it is
2. Change the division sign to multiplication
3. Flip the second fraction (swap numerator and denominator)

Worked example: 3⁄4 ÷ 1⁄2

• Keep: 3⁄4
• Change: ÷ becomes ×
• Flip: 1⁄2 becomes 2⁄1
• 3⁄4 × 2⁄1 = 6⁄4 = 1 1⁄2

This makes intuitive sense: how many halves fit into three-quarters? One and a half.

Dividing a fraction by a whole number is common in KS2 SATs:

2⁄5 ÷ 3 = 2⁄5 × 1⁄3 = 2⁄15

Tip: “Keep, Change, Flip” is easy to remember but make sure your child understands what division by a fraction means conceptually — “How many [second fraction]s fit into [first fraction]?” — not just the procedure.

Mixed Numbers and Improper Fractions

A mixed number combines a whole number and a fraction: 2¾ means two wholes and three quarters.

An improper fraction has a numerator larger than its denominator: 11⁄4 means eleven quarters.

They are equivalent: 2¾ = 11⁄4.

Converting mixed to improper

Multiply the whole number by the denominator, add the numerator, put the result over the original denominator:

2¾ → (2 × 4) + 3 = 11 → 11⁄4

Converting improper to mixed

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator:

17⁄5 → 17 ÷ 5 = 3 remainder 2 → 3 2⁄5

Children need to be comfortable converting in both directions — many SATs questions require giving answers as mixed numbers or as improper fractions, and children need to recognise when each form is appropriate.

Fractions, Decimals, and Percentages

These three are all different ways of expressing parts of a whole. Year 5 and 6 children are expected to convert fluently between them — this is a major SATs topic.

How to convert

• Fraction → decimal: Divide the numerator by the denominator. 3⁄8 → 3 ÷ 8 = 0.375
• Decimal → percentage: Multiply by 100. 0.375 → 37.5%
• Percentage → fraction: Put over 100 and simplify. 35% → 35⁄100 → 7⁄20
• Fraction → percentage (shortcut): If the denominator is a factor of 100, scale up. 3⁄5 → multiply both by 20 → 60⁄100 = 60%

Children should know the common equivalences in the table above by heart — they appear frequently in SATs and save valuable time.

Fractions of Amounts

Finding a fraction of an amount is one of the most common question types in KS2 SATs, both in the arithmetic paper and reasoning papers.

The method: divide by the denominator, then multiply by the numerator.

Worked example: Find 3⁄5 of 45

• Step 1: 45 ÷ 5 = 9 (find one fifth)
• Step 2: 9 × 3 = 27 (find three fifths)
• Answer: 27

Worked example: Find 2⁄7 of 63

• Step 1: 63 ÷ 7 = 9
• Step 2: 9 × 2 = 18
• Answer: 18

SATs reasoning papers often embed fractions-of-amounts in word problems: “A school has 120 pupils. 3⁄8 of them walk to school. How many pupils walk?” Children need to extract the fraction and the amount from the context.

What's Taught in Each Year

Fractions are introduced gradually across KS1 and KS2. Understanding where your child is on this progression helps you pitch your support at the right level.

Source: National curriculum in England: mathematics programmes of study (DfE, 2014)

Common Mistakes Children Make

• Adding denominators: 1⁄3 + 1⁄4 = 2⁄7 ✗ — this is the single most common fractions error. The denominator defines the size of the parts; you can't add parts of different sizes without converting first
• Thinking bigger denominator = bigger fraction: 1⁄8 is smaller than 1⁄3, not bigger. More parts means each part is smaller
• Forgetting to simplify: SATs questions often require answers in their simplest form. 4⁄8 should be given as 1⁄2
• Not converting mixed numbers for calculations: To add 2 1⁄3 + 1 3⁄4, children should convert to improper fractions first (7⁄3 + 7⁄4), find a common denominator, then convert back to a mixed number
• Confusing fraction operations: Children sometimes apply multiplication rules to addition (or vice versa). Clear, separate practice of each operation helps prevent mixing them up

Frequently Asked Questions