KS3

Fractions, Decimals & Percentages

A parent's guide to fractions, decimals and percentages — what they are, how schools teach them, and how to help.

What Your Child Is Learning

Fractions, decimals and percentages are three different ways of writing the same thing. Half a pizza can be written as \(\frac{1}{2}\), or 0.5, or 50%. Your child is learning that these are all equivalent — and that being able to switch between them is one of the most useful maths skills there is.

A fraction is a part of a whole. The top number (numerator) says how many parts you have. The bottom number (denominator) says how many equal parts the whole has been split into. So \(\frac{3}{4}\) means "3 out of 4 equal parts."

Schools teach all three forms together because they come up everywhere in real life. Discounts are given as percentages. Measurements use decimals. Recipes use fractions. Your child needs to move fluently between them.

Fraction	Decimal	Percentage
\(\frac{1}{2}\)	0.5	50%
\(\frac{1}{4}\)	0.25	25%
\(\frac{3}{4}\)	0.75	75%
\(\frac{1}{5}\)	0.2	20%
\(\frac{1}{10}\)	0.1	10%
\(\frac{1}{3}\)	0.333...	33.3...%

How Schools Teach It Now

Schools use three main tools: bar models for fractions, place value grids for decimals, and the "of means multiply" rule for percentages.

Bar models for fractions: A bar model is a rectangle split into equal parts. To show \(\frac{3}{4}\), draw a rectangle, divide it into 4 equal parts, and shade 3 of them. This makes the fraction visible and concrete.

Place value for decimals: Your child learns that the digit after the decimal point is tenths, the next is hundredths. So 0.35 means 3 tenths and 5 hundredths. This connects decimals to the place value system they already know.

Percentages — "of means multiply": To find a percentage of an amount, schools teach building from 10% and 1%. Here's how they'd find 35% of 80:

Find 10%. Divide by 10. \(10\%\text{ of }80 = 8\).
Find 30%. Multiply your 10% by 3. \(30\% = 8 \times 3 = 24\).
Find 5%. Half of 10%. \(5\% = 8 \div 2 = 4\).
Add them together. \(35\% = 30\% + 5\% = 24 + 4 = 28\).

This "building blocks" method is powerful because it works for any percentage without a calculator.

Common Mistakes to Watch For

Adding fractions by adding tops and bottoms. If your child writes \(\frac{1}{2} + \frac{1}{3} = \frac{2}{5}\), they've added the numerators and denominators separately. This is wrong. You need a common denominator first: \(\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}\).
Thinking 0.25 is bigger than 0.3 because 25 is bigger than 3. Compare in hundredths: 0.30 against 0.25, and 30 beats 25.
Dividing by the percentage number (\(60 \div 20 = 3\)) doesn't find 20%. It only happens to work for 10%. To find 20%, find 10% (6) and double it: 12.
Confusing "of" with "out of." \(\frac{3}{4}\) means "3 out of 4" (a fraction). But "find \(\frac{3}{4}\) of 20" means multiply: \(\frac{3}{4} \times 20 = 15\). The word "of" in maths almost always means multiply.

Try It Together

The Problem

What is 35% of £80?

Step 1: Find 10% — divide by 10. \(10\%\text{ of }80 = 8\).

Step 2: Find 30% — multiply 10% by 3. \(30\% = 8 \times 3 = 24\).

Step 3: Find 5% — halve 10%. \(5\% = 8 \div 2 = 4\).

Step 4: Add them. \(35\% = 24 + 4 = \mathbf{28}\).

Answer: 35% of £80 is £28.

Try another: what is 15% of £60? (Answer: 10% = £6, 5% = £3, so 15% = £9.)

Let Them Practise

These free games let your child practise fractions and percentages.

Play Fraction Equivalence → Play Percentage Flip →

MaffsGames needs no account and no sign-up; what it records while your child plays is set out on the privacy page.

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