The two numbers in a fraction
Every fraction has two numbers separated by a fraction bar:
| Part | Where | Tells you | In 3/4 |
|---|---|---|---|
| Numerator | top | How many parts we’re counting | 3 |
| Denominator | bottom | How many equal parts make one whole | 4 |
A memory trick: Denominator is Down; and the denominator names the kind of part (fourths, fifths, tenths), like a noun. The numerator numbers how many of them we have.
Reading fractions
| Fraction | Say |
|---|---|
| 1/2 | one half |
| 2/3 | two thirds |
| 3/4 | three quarters (or three fourths) |
| 5/8 | five eighths |
| 7/10 | seven tenths |
The denominator controls the size of the parts
The bigger the denominator, the more pieces the whole is cut into, so each piece is smaller.
- 1/2 of a pizza is bigger than 1/8 of the same pizza.
A unit fraction has a numerator of 1: 1/2, 1/3, 1/10. Every other fraction is made of unit fractions. For example, 3/5 = 1/5 + 1/5 + 1/5.
The numerator counts the parts
With the same denominator, a bigger numerator means a bigger fraction: 4/7 > 2/7.
Special cases
| Fraction | What it means |
|---|---|
| 0/5 | none of the parts: equal to 0 |
| 5/5 | all the parts: equal to 1 whole |
| 7/5 | more than one whole (an improper fraction) |
| 5/0 | not allowed: you can’t cut a whole into 0 parts |
The fraction bar means divide
The fraction 3/4 also means 3 ÷ 4. If 3 pizzas are shared among 4 people, each gets 3/4 of a pizza. This link between fractions and division is used all through maths.
Worked examples
Example 1: In 5/9, what is the numerator and what does it mean?
The numerator is 5: we are counting 5 parts.
Example 2: A chocolate bar has 12 equal pieces. You eat 5. Write the fraction you ate.
Denominator = 12 pieces in the whole. Numerator = 5 eaten. 5/12.
Example 3: Which is bigger: 1/6 or 1/4?
Same numerator; the smaller denominator means bigger parts. 1/4 is bigger.
Common mistakes
- Swapping the numerator and denominator. The whole goes on the bottom.
- Thinking a bigger denominator means a bigger fraction. It means smaller pieces.
- Counting unequal parts. The denominator only works when parts are equal.
Try it yourself
- Name the denominator in 7/12.
- A flag has 6 equal stripes; 4 are red. What fraction is red?
- What fraction equals one whole with a denominator of 3?
- Which is smaller: 1/10 or 1/5?
Answers: 1) 12 2) 4/6 3) 3/3 4) 1/10
Quick recap
- The numerator counts parts; the denominator says how many equal parts make a whole.
- Bigger denominator → smaller pieces.
- The fraction bar also means "divided by".