7.5 Fractions & Percentages

Find a fraction equivalent to $\dfrac{2}{3}$ with a denominator greater than 50. Justify that it is equivalent.

Simplify $\dfrac{8}{12}$ fully. State the HCF you used and why dividing by it gives the simplest form.

Which fraction is larger: $\dfrac{7}{10}$ or $\dfrac{4}{10}$? Justify by explaining what the numerator tells you.

Calculate $\dfrac{2}{5} + \dfrac{1}{5}$ and simplify your answer. Explain why the denominator does not change when adding.

Calculate $\dfrac{5}{6} - \dfrac{1}{6}$ in its simplest form. Check your answer by adding back.

Find $\dfrac{1}{4}$ of 32. Explain why you divide by the denominator to find a unit fraction of an amount.

Find 50% of 60 in two different ways. Show both methods give the same answer.

Write 2$\,\dfrac{3}{4}$ as an improper fraction. Justify by explaining what each whole number contributes.

Write $\dfrac{9}{4}$ as a mixed number. Check by converting back to an improper fraction.

Write $\dfrac{1}{4}$ as a decimal. Explain the connection between the fraction and the decimal.

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

Calculate $\dfrac{5}{6} - \dfrac{1}{4}$. Give your answer in its simplest form.

Calculate $\dfrac{3}{5} \times \dfrac{5}{6}$. Give your answer in its simplest form.

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

Find $\dfrac{2}{5}$ of 60.

Write 60% as (a) a decimal and (b) a fraction in its simplest form.

Find 30% of 90.

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

Write $\dfrac{1}{2}$, $\dfrac{3}{8}$, and $\dfrac{5}{12}$ in order from smallest to largest.

Increase £60 by 15%.

Find the HCF of 30 and 42, then use it to simplify $\dfrac{30}{42}$ fully.

What is 15% of −£60?

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

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

Decrease £200 by 45%.

Write $\dfrac{2}{9}$ as a decimal. State whether it is terminating or recurring.

Write $-\dfrac{3}{4}$ and $-\dfrac{5}{8}$ in order from smallest to largest.

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

Find $\dfrac{5}{6}$ of 3 m. Give your answer in centimetres.

35% of a number is 63. What is the number?

A jacket costs £120. It is reduced by 20% and then by a further 15%. What is the final price?

After a 25% increase, a price is £90. What was the original price?

Solve $\dfrac{3}{4} \times x = 18$.

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

Calculate $2\,\dfrac{2}{3} + 1\,\dfrac{3}{4} - \dfrac{5}{6}$.

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

Convert the recurring decimal $0.\overline{63}$ to a fraction in its simplest form.

A price changes from £60 to £45. Find the percentage change and state whether it is an increase or decrease.

$\dfrac{5}{8}$ of a class of 48 students passed a test. Of those who passed, $\dfrac{3}{5}$ also completed the homework. How many students both passed and completed the homework?

Shop A sells 250g of cereal for £0.90. Shop B sells the same cereal: 400g for £1.32. Which is the better value? Show your working.