GCSE Fractions of amounts Practice Questions

Divide by the denominator

To find a half of an amount you split it into $2$ equal parts, and dividing by $2$ does exactly that. Remember from the division topic that dividing shares a number into equal groups.

Read off one part

One half is a single one of those $2$ equal parts, so the division already gives the answer.

State the answer

So a half of $18$ is $9$.

Divide by the denominator

To find a half of an amount you split it into $2$ equal parts, and dividing by $2$ does exactly that. Remember from the division topic that dividing shares a number into equal groups.

Read off one part

One half is a single one of those $2$ equal parts, so the division already gives the answer.

State the answer

So a half of $46$ is $23$.

Plan: work from the inside out

Deal with the inner "of" first, then take the outer fraction of that result. "Of" always means multiply.

Find $\frac{3}{4}$... the inner fraction of the amount

Split $40$ into $4$ equal parts to start finding $3$ quarters.

Complete the inner fraction

Multiply by $3$ to get $3$ quarters of $40$, which is $30$.

Take the outer fraction of that

Now find $2$ fifths of $30$ the same way: divide by $5$, multiply by $2$.

Sense check by multiplying the fractions first

Multiplying the two fractions gives $\frac{3}{10}$; taking that of $40$ gives the same $12$.

State the answer

The final answer is $12$.

Plan the comparison

Work out each amount fully, then find the difference. Comparing the actual amounts, not the fractions, is what matters.

Divide for the first amount

One fifth of $60$ is $12$.

Complete the first amount

$2$ fifths of $60$ is $24$.

Divide for the second amount

One third of $54$ is $18$.

Complete the second amount

$1$ thirds of $54$ is $18$.

Decide which is larger

The larger amount is $24$.

Subtract to find the difference

The difference between them is $6$.

Sense check

Adding the difference to the smaller amount returns the larger one.

Watch out for the common error

You cannot just compare the fractions; the totals are different, so you must work out both amounts.

State the answer

The final answer is $6$ pounds.

Plan the stages

Each fraction is spent from the money remaining at that point. Work stage by stage to the amount left.

charity: spend the fraction

$1$ ninths of $2160$ is $240$ for charity.

Money left after charity

$1920$ remains after paying charity.

rent: spend the fraction

$5$ twelfths of $1920$ is $800$ for rent.

Money left after rent

$1120$ remains after paying rent.

food: spend the fraction

$1$ quarters of $1120$ is $280$ for food.

Money left after food

$840$ remains after paying food.

State the final amount left

After all three, $840$ is left.

Sense check

The three amounts plus what is left add back to $2160$.

Check the amount after the first stage

After the first spend $1920$ remained, which the next fraction used.

Watch out for the common error

Only the first fraction is of the full amount; the later ones are of what is left.

Interpret the last stage

The final spend was a fraction of the $1120$ left before it.

Alternative for the last stage

Keeping the other fraction of the $1120$ gives the $840$ left directly.

Note the answer is exact

Every step used exact whole numbers or fractions, so there is no rounding — the answer is exact.

State the answer

The final answer is $840$ pounds.