Three kinds of wholes
A fraction describes part of a whole. That whole can be:
| Whole | Example | ¾ means |
|---|---|---|
| A shape | a pizza | 3 of 4 equal slices |
| A set | a group of 12 marbles | 3 out of every 4 marbles: 9 marbles |
| A quantity | a 1-metre ribbon, 60 minutes | 75 cm; 45 minutes |
Fractions of shapes
Divide the shape into equal parts. The denominator is the number of equal parts; the numerator is how many are shaded.
A rectangle split into 5 equal strips with 2 shaded shows 2/5.
Remember: the parts must be equal in size. A circle cut into 4 unequal pieces doesn’t show quarters.
Fractions of a set
In a set, each object is a part. If 3 of 8 balloons are red, then 3/8 of the balloons are red.
The objects don’t have to be the same size. One big balloon and one small balloon each count as 1 out of the set.
Fractions of a quantity
To find a fraction of a number:
- Divide by the denominator (to find one part).
- Multiply by the numerator (to find that many parts).
Example: ¾ of 20
- 20 ÷ 4 = 5 (one quarter)
- 5 × 3 = 15 (three quarters)
Using a bar model
A bar model makes this clear. For ⅔ of 18:
| 6 | 6 | 6 |
|---|
The bar of 18 is split into 3 equal parts of 6. Two parts = 12.
Fractions of time and measurement
- ½ of an hour = 30 minutes
- ¼ of an hour = 15 minutes
- ½ of a metre = 50 cm
- ¾ of a kilogram = 750 g
Worked examples
Example 1: What fraction of the letters in MATH are vowels?
1 vowel (A) out of 4 letters → 1/4.
Example 2: Find ⅖ of 35.
35 ÷ 5 = 7; 7 × 2 = 14.
Example 3: 24 students; ⅝ walk to school. How many walk?
24 ÷ 8 = 3; 3 × 5 = 15 students.
Common mistakes
- Unequal parts in a shape.
- Dividing by the numerator instead of the denominator.
- Forgetting the second step (multiplying by the numerator).
- Counting the wrong total in a set: the denominator is the whole set, not just the other group.
Try it yourself
- ⅓ of 27
- ¾ of 40
- 5 of 9 cubes are blue. What fraction are not blue?
- How many minutes are ⅔ of an hour?
Answers: 1) 9 2) 30 3) 4/9 4) 40
Quick recap
- A fraction can describe part of a shape, a set or a quantity.
- Denominator = equal parts in the whole; numerator = parts counted.
- To find a fraction of a number: divide by the denominator, multiply by the numerator.