Fractions
Understanding fractions
A fraction shows equal parts of a whole. You see fractions all around you — sharing a cake, or working out a half-price sale.
The two numbers in a fraction
A fraction has two numbers. The bottom number is the denominator — it tells you how many equal parts the whole is split into. The top number is the numerator — it tells you how many of those parts you have. Example: 3/4 means 3 parts out of 4 equal parts. We read it as 'three-quarters'.
Equal parts
When you divide a shape into a fraction, every part must be the same size. The parts can be in different positions, but they must all be equal. Eight people sharing one cake equally each get one-eighth (1/8) of the cake.
More parts means smaller pieces
The more equal parts a whole is divided into, the smaller each part is. That is why 1/3 is smaller than 1/2 — the whole is split into 3 equal parts instead of 2. And 1/8 is smaller than 1/6.
A fraction is a division
A fraction can be written as the numerator divided by the denominator. For example, 3/4 is the same as 3 ÷ 4, and a hexagon split into 4 equal parts shows 1 ÷ 4 = 1/4.
Worked examples
Naming the fraction shaded
- A shape is divided into 6 equal parts.
- 2 of the parts are shaded.
- The denominator is 6 (equal parts); the numerator is 2 (shaded parts).
Answer: Two-sixths (2/6) of the shape is shaded.
Sharing to make a fraction
- One cake is shared equally between 8 people.
- The cake is cut into 8 equal parts.
- Each person gets 1 of the 8 parts.
Answer: Each person gets one-eighth (1/8) of the cake.
Comparing unit fractions
- Compare 1/3 and 1/2.
- 1/3 splits the whole into 3 equal parts; 1/2 into 2 equal parts.
- More parts means each part is smaller.
Answer: 1/3 is smaller than 1/2.
A fraction as a division
- Write 3/4 as a division.
- The fraction is the numerator divided by the denominator.
Answer: 3/4 = 3 ÷ 4.
Where you see this in real life
- Sharing a cake equally between friends.
- Working out a half-price sale, for example $20 becomes $10.
- Cutting a pizza into equal slices.
Key words
- Fraction
- A number that shows equal parts of a whole, such as 3/4.
- Numerator
- The top number of a fraction — how many parts you have.
- Denominator
- The bottom number — how many equal parts the whole is split into.
- Equal parts
- Parts that are all the same size.
- Unit fraction
- A fraction with a numerator of 1, such as 1/5.