Fractions (Edexcel GCSE Maths: Higher): Exam Questions

Work out  $1\frac{1}{5}\times 2\frac{1}{3}$

Give your answer as a mixed number in its simplest form.

Work out  $2\frac{7}{15}-1\frac{2}{3}$

Work out  $2\frac{1}{7}+1\frac{1}{4}$

Work out  $1\frac{1}{5}÷\frac{3}{4}$

Give your answer as a mixed number in its simplest form.

Ceri worked out $\frac{3}{5}\times 4$

She wrote:

$\frac{3\times 4}{5\times 4}=\frac{12}{20}$

The answer $\frac{12}{20}$ is wrong.

Describe the mistake that Ceri made.

Zak worked out $\frac{15}{22}÷\frac{3}{11}$

He wrote:

$15÷3=5$ and $22÷11=2$

so $\frac{15}{22}÷\frac{3}{11}=\frac{5}{2}$

The answer of $\frac{5}{2}$ is wrong.

Describe the mistake that Zak made.

Work out  $3\frac{1}{2}\times 1\frac{3}{5}$
Give your answer as a mixed number in its simplest form.

Show that  $6\frac{3}{4}÷2\frac{4}{7}=2\frac{5}{8}$

Show that   $3\frac{1}{5}\times 1\frac{5}{6}=5\frac{13}{15}$

Show that  $2\frac{4}{7}÷1\frac{1}{8}=2\frac{2}{7}$

Show that  $4\frac{2}{3}+3\frac{4}{5}=8\frac{7}{15}$

Show that   $3\frac{1}{5}\times 2\frac{5}{8}=8\frac{2}{5}$

Show that  $4\frac{2}{3}÷1\frac{1}{9}=4\frac{1}{5}$

Show that  $3\frac{4}{7}-1\frac{5}{8}=1\frac{53}{56}$

The range of a set of numbers is $15\frac{1}{4}$
The smallest number is $–2\frac{7}{8}$
Work out the largest number.

Choose the number half way between  $\frac{7}{12}$ and $\frac{3}{4}$

Work out the value of  ${\left(1\frac{2}{3}\right)}^2$

Work out  $8\frac{1}{2}÷2\frac{2}{3}$

Give your answer as a mixed number.

Work out  $2\frac{3}{4}\times 1\frac{5}{7}$

Give your answer as a mixed number in its simplest form.

In a school, $\frac{2}{3}$ of the students study a language. Of those students who study a language, $\frac{2}{5}$ study Spanish.

Find the ratio of students who study Spanish to students who do not study Spanish.

A unit fraction has a numerator equal to 1, for example $\frac{1}{3},\frac{1}{7}$ and $\frac{1}{25}$.

Unit fractions can be written as the sum of two different unit fractions, for example

$\frac{1}{2}=\frac{1}{3}+\frac{1}{6}$

Write each of the following unit fractions as the sum of two different unit fractions.

$\frac{1}{4}=\frac{1}{\square }+\frac{1}{\square }$

$\frac{1}{5}=\frac{1}{\square }+\frac{1}{\square }$

$\frac{1}{6}=\frac{1}{\square }+\frac{1}{\square }$

Work out $1\frac{1}{4}÷\frac{2}{7}$

Using algebra, prove that $2.03\dot{7}$ can be written as $\frac{917}{450}$

Work out  $2\frac{1}{4}\times 3\frac{1}{3}$

Give your answer as a mixed number in its simplest form.

Write the numbers 3, 4, 5 and 6 in the boxes to give the greatest possible total.

You may write each number only once.

$\boxed{}\frac{1}{\boxed{}}+\boxed{}\frac{2}{\boxed{}}$

Show that $1\frac{2}{3}+2\frac{3}{4}=4\frac{5}{12}$

There are $60$ children in a club.

In the club, the ratio of the number of girls to the number of boys is $3:1$

$\frac{3}{5}$ of the girls play a musical instrument.

$\frac{4}{5}$ of the boys play a musical instrument.

What fraction of the $60$ children play a musical instrument?

Show that $5\frac{2}{3}-2\frac{3}{4}=2\frac{11}{12}$

Each month Edna spends all her income on rent, on travel and on other living expenses.

She spends $\frac{1}{3}$ of her income on rent.

She spends $\frac{1}{5}$ of her income on travel.

She spends $\$420$ of her income on other living expenses.

Work out her income each month.

A shopkeeper compares the income from sales of a laptop in March and April.

April

By what fraction does the income from these sales decrease in April?

A ball is thrown from a height of 15 metres.

It bounces to height $h_1$, then to height $h_2$ as shown.

$h_1$ is three quarters of the original height.

Jack expects $h_2$ to be three quarters of $h_1$

Work out the value of $h_2$ that he expects.

.........................metres

In fact, $h_2$ is two thirds of $h_1$

How does this affect the answer to part (a)? Tick a box.

$\square$      The ball bounced higher than he expected

$\square$        The ball bounced lower than he expected

Show working to support your answer.

In an office there are twice as many females as males.

$\frac{1}{4}$ of the females wear glasses.

 $\frac{3}{8}$ of the males wear glasses.

84 people in the office wear glasses.
Work out the number of people in the office.

Charlie and Jasmine share cartons of apple juice.

Charlie drinks $\frac{1}{3}$ of a carton every day.

Jasmine drinks $\frac{2}{5}$ of a carton every day.

Any apple juice left in a carton at the end of the day is used the following day.

The cost of a carton is 70p.
Charlie and Jasmine buy just enough cartons to last them for 10 days.

How much do they spend in total for these cartons?
Give your answer in £. Show your working.

£ .......................................................

Mrs Mills buys $4$ packs of treats for her cats, Fluff and Tigger.
She gives Fluff $\frac{1}{6}$ of a pack each day.

She gives Tigger $\frac{1}{5}$ of a pack each day.

For how many complete days will the $4$ packs of treats last?

Sally has $30$ feet of ribbon.

She cuts strips each of length  $2\frac{2}{5}$ feet from the ribbon.

Sally says

      I can cut $13$ of these strips from this ribbon.

Is she correct? Show how you decide.