Fractions (Edexcel IGCSE Maths A: Higher): Exam Questions

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

Show that $2\frac{7}{15}-1\frac{2}{3}=\frac{4}{5}$

Show that $2\frac{1}{7}+1\frac{1}{4}=3\frac{11}{28}$

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

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

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

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

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.

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

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

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

Without using a calculator, work out  $\frac{15}{28}÷\frac{4}{7}$.

You must show all your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out  $\frac{2}{3}+\frac{1}{4}\times \frac{2}{3}$.
Write down all the steps of your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out $\frac{5}{6}+\frac{2}{3}.$
You must show all your working and give your answer as a mixed number in its simplest form.

Giulio’s reaction times are measured in two games.
In the first game his reaction time is $\frac{1}{3}$ of a second.
In the second game his reaction time is $\frac{1}{8}$ of a second.  

Find the difference between the two reaction times.  

.................................................. s

Without using a calculator, work out $\frac{12}{35}\times \frac{7}{9}$.
You must show all your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out  $\frac{1}{15}+\frac{2}{5}$.
Write down all the steps of your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out  $\frac{1}{4}÷\frac{2}{3}$.
You must show all your working and give your answer as a fraction.

Collette has $136 and spends half of her money on clothes and $\frac{1}{5}$ of her money on books.

Calculate the amount she has left.

$ ...............................................

Without using your calculator, work out $\frac{2}{3}-\frac{1}{12}$.

You must show all your working and give your answer as a fraction in its simplest form.

Without using your calculator, work out $\frac{7}{8}+\frac{1}{6}$.

You must show all your working and give your answer as a mixed number in its simplest form.

Show that $4\frac{2}{3}÷1\frac{1}{5}=3\frac{8}{9}$

Show that $3\frac{3}{7}÷2\frac{2}{3}=1\frac{2}{7}$

Show that $2\frac{1}{4}\times 3\frac{1}{3}=7\frac{1}{2}$

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

You may write each number only once.

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 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.

Without using a calculator, work out $\frac{5}{6}÷1\frac{1}{3}$.

You must show all your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out  $2\frac{2}{3}\times 2\frac{3}{4}$.

You must show all your working and give your answer as a mixed number in its simplest form.

Without using a calculator, work out $1\frac{1}{7}\times 2\frac{1}{10}$.

You must show all your working and give your answer as a mixed number in its simplest form.

Without using a calculator, work out  $\left(2\frac{1}{3}-\frac{7}{8}\right)\times \frac{6}{25}.$

You must show all your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out $1\frac{3}{4}-\frac{11}{12}.$
You must show all your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out $3\frac{1}{4}-2\frac{2}{3}$.

You must show all your working and give your answer as a fraction in its simplest form.

Without using your calculator, work out  $1\frac{7}{12}+\frac{13}{20}$.
You must show all your working and give your answer as a mixed number in its simplest form.

Without using a calculator, work out  $\frac{5}{16}\times 1\frac{1}{7}$.

You must show all your working and give your answer as a fraction in its simplest form.

Without using a calculator, workout  $3\frac{5}{8}-1\frac{2}{3}$.

You must show all your working and give your answer as a mixed number in its simplest form.

Without using a calculator, work out  $2\frac{1}{4}÷\frac{3}{7}$ . 

You must show all your working and give your answer as a mixed number in its simplest form. 

Without using a calculator, work out $3\frac{1}{8}÷\frac{5}{12}$.

You must show all your working and give your answer as a mixed number in its simplest form.

Without using your calculator, work out  $\frac{3}{8}÷2\frac{1}{4}$.

You must show all your working and give your answer as a fraction in its simplest form.

Without using your calculator, work out  $1\frac{3}{4}\times \frac{6}{35}$.

You must show all your working and give your answer as a fraction in its simplest form.

Without using a calculator, work out $\frac{2}{3}÷1\frac{1}{5}$.

You must show all your working and give your answer as a fraction in its simplest form.