Maths
What is a fraction?
Quick answer
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
In one sentence
A fraction tells you how many equal parts of a whole you have.
Explained
Cut a cake into 4 equal pieces. Each piece is one quarter, written ¼. Take 3 pieces and you have three quarters, ¾.
cake
pizza
orange
Every fraction has two numbers:
- The denominator (bottom) says how many equal parts the whole is split into.
- The numerator (top) says how many of those parts you have.
The word equal matters. If you cut a sandwich into one big bit and one tiny bit, neither piece is a half.
Here is a surprise: the bigger the denominator, the smaller each piece. One third of a pizza is more than one fifth of the same pizza, because sharing between 5 people leaves smaller slices than sharing between 3.
A fraction can also be a part of a group of things. To find ⅓ of 15 marbles, split them into 3 equal groups: 15 ÷ 3 = 5. To find ⅔, take two of those groups: 10. This is why fractions and division are so closely linked. In fact ¾ means 3 ÷ 4.
When the top number is bigger than the bottom, like 7/4, the fraction is more than a whole. It is called an improper fraction, and it can be written as a mixed number: 1¾. Different fractions can also be the same size, like ½ and 2/4. See equivalent fractions.
Examples
| Fraction | Say it | Picture |
|---|---|---|
| ½ | one half | 1 of 2 equal parts |
| ⅓ | one third | 1 of 3 equal parts |
| ¾ | three quarters | 3 of 4 equal parts |
| 5/8 | five eighths | 5 of 8 equal parts |
| 9/4 | nine quarters | 2¼ wholes |
Worked example: ⅖ of 30. One fifth is 30 ÷ 5 = 6, so two fifths is 12.
Common mistakes
- Thinking 1/8 is bigger than 1/4 because 8 is bigger than 4. Fix: draw both on the same-sized bar.
- Unequal parts. Fix: always check the pieces are the same size before naming the fraction.
- Adding tops and bottoms, so ½ + ¼ = 2/6. Fix: make the denominators the same first. ½ = 2/4, so 2/4 + ¼ = ¾.
Quick quiz
Fractions
Check what you know with 5 quick questions.
Question 1 of 5
A pizza is cut into 8 equal slices and you eat 3. What fraction did you eat?
Practise it
Try it
Fraction worksheets
Practise it step by step in a full course: Grade 4 Maths
For grown-ups
Related topics
Equivalent fractions
Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.
Decimals
Decimals are numbers with a decimal point. Digits after the point show tenths, hundredths and so on, so 2.5 means two and five tenths.
Percentages
A percentage is a number out of 100, written with the sign %. So 25% means 25 out of every 100, which is the same as one quarter.
Division
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
Adding and subtracting fractions
To add or subtract fractions, first give them the same denominator. Then add or subtract only the numerators and keep the denominator. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Comparing fractions
To compare fractions, check whether they share a denominator or a numerator, or rewrite them with a common denominator. The bigger fraction is the one with more of the whole.