P4 Fraction of a Set

A fraction can describe a group of objects, not just a shaded strip. Think of twenty stickers shared into four equal piles: the denominator tells you how many piles, and the numerator tells you how many piles to take.

Parents: ask your child to make the equal groups aloud before they count the selected objects.

By the end you will be able to find a fraction of a set by partitioning a divisible set into equal groups and selecting whole groups.

Make equal groups first

To find $\frac{3}{4}$ of twenty, divide twenty objects into four equal groups. Each group has five objects. Select three groups, giving fifteen objects. The denominator is doing the sharing; it is not an instruction to divide the final answer by itself.

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Fraction of a set: make equal groups

🤔 Predict first: How many objects are $\frac{3}{4}$ of 20?

10 objects15 objects20 objects

Find a fraction of a set

$$20 \div 4 = 5$$

$$5 \times 3 = 15$$

$$\frac{3}{4} \text{ of } 20 = 15$$

Read the numerator and denominator

The denominator tells you how many equal groups make the whole set. The numerator tells you how many of those groups are chosen. For $\frac{2}{5}$ of twenty-five, make five groups of five and select two groups.

Find a fraction of a set

$$25 \div 5 = 5$$

$$5 \times 2 = 10$$

$$\frac{2}{5} \text{ of } 25 = 10$$

For the specified P4 example, $\frac{3}{5}$ of twenty-five also uses five equal groups of five. Select three groups: $\frac{3}{5}$ of 25 = 15.

Find a fraction of a set

$$25 \div 5 = 5$$

$$5 \times 3 = 15$$

$$\frac{3}{5} \text{ of } 25 = 15$$

Check with a second representation

You can also imagine each object receiving a fraction label. When the set divides evenly, the group method is quick and clear. For $\frac{3}{4}$ of twenty, four groups of five account for all twenty objects, and three chosen groups account for fifteen.

Check the whole set

$$4 \times 5 = 20$$

$$3 \times 5 = 15$$

$$\frac{3}{4} \text{ of } 20 = 15$$

Practise with worked steps

Practice 1: Find $\frac{3}{4}$ of twenty

Divide, then select

$$20 \div 4 = 5$$

$$5 \times 3 = 15$$

$\frac{3}{4}$ of twenty is 15 objects.

Practice 2: Find $\frac{2}{5}$ of twenty-five stickers

Make five equal groups

$$25 \div 5 = 5$$

$$5 \times 2 = 10$$

$\frac{2}{5}$ is 10 stickers.

Practice 3: Find $\frac{2}{5}$ of thirty-five cards

Transfer the group method

$$35 \div 5 = 7$$

$$7 \times 2 = 14$$

$\frac{2}{5}$ is 14 cards.

Watch out — easily mixed up

Follow the fraction path

Use P3 equivalent fractions to rename the fraction when the parts change. For operations on fraction amounts, continue to P4 fraction addition and subtraction.

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. What is $\frac{3}{4}$ of twenty?

   15517

2. What is $\frac{2}{5}$ of twenty-five?

   15105

3. What is $\frac{3}{5}$ of fifteen?

   1239

4. What should you do first to find $\frac{4}{7}$ of twenty-one?

   Divide 21 by 7.Multiply 21 by 4.Subtract 7 from 21.

5. A box has forty cards. $\frac{3}{8}$ are animal cards. How many animal cards are there?

   121518

6. A class has twenty-five stickers. $\frac{2}{5}$ are blue. How many are blue?

   51015

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