Fractions, Decimals and Percentages: How They Connect
By the TimesTable.co team · Updated · 3 min read
Children often learn fractions, decimals and percentages as three separate topics, in three separate years, and never quite realise they're the same thing. Half a pizza, 0.5 of a pizza and 50% of a pizza are exactly the same amount of pizza. Once that clicks, conversion stops being a set of rules to memorise and starts making sense.
Why are they the same amount?
Each is a way of describing part of a whole:
- A fraction splits the whole into equal parts: ½ is one of two equal parts.
- A decimal uses place value (tenths, hundredths): 0.5 is five tenths.
- A percentage always splits into 100 parts: 50% is 50 out of 100.
Our fractions, decimals and percentages explorer shows all three side by side (a pie, a hundred grid and a percentage bar), and changing one updates the others. It's the quickest way for a child to see the connection.
How do you convert between them?
| From → To | How | Example |
|---|---|---|
| Fraction → Decimal | Divide top by bottom | ¾ = 3 ÷ 4 = 0.75 |
| Decimal → Percentage | Multiply by 100 | 0.75 → 75% |
| Percentage → Fraction | Put over 100, simplify | 75% = 75/100 = ¾ |
| Percentage → Decimal | Divide by 100 | 75% → 0.75 |
The fraction-to-decimal step is a division: for ⅛ it's 1 ÷ 8 = 0.125, which children can work out with the bus stop method.
Which ones should be learnt by heart?
| Fraction | Decimal | Percentage |
|---|---|---|
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ¾ | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
| 1/5 | 0.2 | 20% |
| 1/100 | 0.01 | 1% |
| ⅓ | 0.333… | 33.3…% |
What mistakes do children commonly make?
- ¾ = 0.34: writing the two numbers side by side after the point.
- 0.5 = 5%: forgetting that 0.5 is five tenths, which is 50 hundredths.
- 50% = 1/50: confusing "50 out of 100" with "1 out of 50".
- 0.05 = 0.5: ignoring the zero placeholder.
The Match It quiz in our explorer uses exactly these mistakes as wrong answers, then shows the working when one is picked.
What does per cent actually mean?
Per cent comes from Latin per centum, "for each hundred". The same "cent" is in century (100 years) and centimetre (a hundredth of a metre). That one idea, "out of 100", explains every percentage conversion.
How can you practise at home?
- Spot percentages in shops ("25% off") and ask what fraction that is.
- Cut food into equal parts and name them all three ways.
- Use the explorer and the fractions workouts for adding, subtracting, multiplying and dividing fractions.
- Practise decimal column sums with the Decimals levels in addition and subtraction.
Converting fractions to decimals relies on division, so it helps to be confident with long division, and with the times tables behind it through smart practice.
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the top number by the bottom number. ¾ is 3 ÷ 4 = 0.75.
How do you convert a decimal to a percentage?
Multiply by 100: the digits move two places to the left. 0.75 × 100 = 75%.
How do you convert a percentage to a fraction?
Write it over 100 and simplify. 75% = 75/100, and dividing top and bottom by 25 gives ¾.
What does per cent mean?
It means "out of 100", from the Latin per centum. 30% means 30 out of every 100.
Which fraction, decimal and percentage facts should children learn by heart?
The common ones: ½ = 0.5 = 50%, ¼ = 0.25 = 25%, ¾ = 0.75 = 75%, 1/10 = 0.1 = 10%, 1/5 = 0.2 = 20% and 1/100 = 0.01 = 1%.
Why is ⅓ written as 0.333…?
Because 1 ÷ 3 never finishes: the 3s go on forever. As a percentage it is 33.3…%, often rounded to 33%.
When do children learn fractions, decimals and percentages?
In England, decimals and fractions are linked from Year 3 and 4, percentages are introduced in Year 5, and all three are connected in Year 6.