# Fraction and percentage

$$\frac {2} {7}$$ or 'two sevenths' means two parts out of seven.

To find $$\frac {2} {7}$$ of a value, you must first divide by 7 to find what $$\frac {1} {7}$$ is worth, and then multiply by 2.

To find a fraction of an amount:

1. Divide by the
2. Multiply by the
Question

Calculate $$\frac {2} {7}$$ of 84.

24.

1. Divide by the denominator: 84 ÷ 7 = 12
2. Multiply by the numerator: 12 x 2 = 24
Question

There are 30 pupils in a class. $$\frac {1} {5}$$ of pupils play a musical instrument. How many do not play an instrument?

$$\frac {1} {5}$$ of 30 = 30 ÷ 5 = 6 pupils play a musical instrument.

This leaves 30 – 6 = 24 pupils who do not play an instrument.

### Finding the original quantity

2/5 of the people on a bus are children. If there are 4 children on the bus, how many people are there in total?

$$\frac {2} {5}$$ of the value = 4

Divide by 2 to find $$\frac {1} {5}$$

$$\frac {1} {5}$$ of the value = 2

Multiply by 5 to find $$\frac {5} {5}$$ or 1 whole

10 people in total.

Question

I eat $$\frac {3} {8}$$ of a chocolate bar and am left with 20 squares, how many squares were there to begin with?

$$\frac {3} {8}$$ has been eaten, which leaves $$\frac {5} {8}$$

$$\frac {5} {8}$$ = 20 squares (now divide by 5)

$$\frac {1} {8}$$ = 4 squares (now multiply by 8)

1 whole = 32 squares.

Question

Louis’ father increases his pocket money by $$\frac {1} {3}$$. He now receives £26 a month. How much was he receiving originally?

£19.50

$\text {1 whole} + \frac {1} {3} = \frac {3} {3} + \frac {1} {3} = \frac {4} {3}$

$$\frac {4} {3}$$ = £26 (now divide by 4)

$$\frac {1} {3}$$ = £6.50 (now multiply by 3)

1 whole = £19.50