7.5 Fractions & Percentages

Find a fraction equivalent to $\dfrac{1}{2}$ with a denominator greater than 100. Justify that it is equivalent.

Simplify $\dfrac{6}{9}$ fully. State the HCF you used and why dividing by it gives the simplest form.

Which fraction is larger: $\dfrac{5}{8}$ or $\dfrac{3}{8}$? Justify by explaining what the numerator tells you.

Calculate $\dfrac{1}{4} + \dfrac{1}{4}$ and simplify your answer. Explain why the denominator does not change when adding.

Calculate $\dfrac{3}{4} - \dfrac{1}{4}$ in its simplest form. Check your answer by adding back.

Find $\dfrac{1}{3}$ of 24. Explain why you divide by the denominator to find a unit fraction of an amount.

Find 50% of 80 in two different ways. Show both methods give the same answer.

Write 1$\,\dfrac{2}{3}$ as an improper fraction. Justify by explaining what each whole number contributes.

Write $\dfrac{7}{2}$ as a mixed number. Check by converting back to an improper fraction.

Write $\dfrac{1}{2}$ as a decimal. Explain the connection between the fraction and the decimal.

Calculate $\dfrac{1}{2} + \dfrac{1}{3}$. Give your answer in its simplest form.

Calculate $\dfrac{3}{4} - \dfrac{1}{3}$. Give your answer in its simplest form.

Calculate $\dfrac{2}{3} \times \dfrac{3}{4}$. Give your answer in its simplest form.

Calculate $\dfrac{3}{4} \div \dfrac{1}{2}$. Give your answer in its simplest form.

Find $\dfrac{3}{4}$ of 48.

Write 35% as (a) a decimal and (b) a fraction in its simplest form.

Find 25% of 64.

Calculate $1\,\dfrac{1}{2} + 2\,\dfrac{1}{4}$.

Write $\dfrac{2}{3}$, $\dfrac{3}{5}$, and $\dfrac{7}{10}$ in order from smallest to largest.

Increase £40 by 20%.

Find the HCF of 18 and 24, then use it to simplify $\dfrac{18}{24}$ fully.

What is 30% of −£40?

Calculate $1\,\dfrac{1}{2} \times 2\,\dfrac{2}{3}$.

Calculate $3\,\dfrac{1}{2} \div 1\,\dfrac{3}{4}$.

Decrease £120 by 35%.

Write $\dfrac{1}{3}$ as a decimal. State whether it is terminating or recurring.

Write $-\dfrac{1}{2}$ and $-\dfrac{2}{3}$ in order from smallest to largest.

Find the value of $3a + 1$ when $a = \dfrac{1}{2}$.

Find $\dfrac{3}{8}$ of 2 m. Give your answer in centimetres.

40% of a number is 48. What is the number?

A jacket costs £80. It is reduced by 25% and then by a further 10%. What is the final price?

After a 20% increase, a price is £72. What was the original price?

Solve $\dfrac{2}{3} \times x = 14$.

Find the value of $a^2 + b$ when $a = \dfrac{3}{4}$ and $b = \dfrac{1}{2}$.

Calculate $2\,\dfrac{3}{4} + 1\,\dfrac{1}{6} - \dfrac{3}{8}$.

Arrange in order from smallest to largest: $-\dfrac{3}{4},\; \dfrac{1}{3},\; -\dfrac{1}{2},\; \dfrac{2}{5}$.

Convert the recurring decimal $0.\overline{3}$ to a fraction in its simplest form.

A price changes from £40 to £52. Find the percentage change and state whether it is an increase or decrease.

$\dfrac{3}{4}$ of a class of 32 students passed a test. Of those who passed, $\dfrac{2}{3}$ also completed the homework. How many students both passed and completed the homework?

Shop A sells 400g of cereal for £1.20. Shop B sells the same cereal: 600g for £1.65. Which is the better value? Show your working.