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 denominator
  2. Multiply by the numerator
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