Year 8 Fractions, decimals and percentages: free practice test with answers

Sample fractions, decimals and percentages questions with answers

Try each one before you open the answer.

1. Equivalent fractions

   Write $\dfrac{84}{126}$ in simplest form.

   Show the answer

   Key idea: Divide the numerator and denominator by their highest common factor.

   1. $84 = 2^2 \times 3 \times 7$ and $126 = 2 \times 3^2 \times 7$, so the HCF is $2 \times 3 \times 7 = 42$
   2. $\dfrac{84 \div 42}{126 \div 42} = \dfrac{2}{3}$

   Answer: $\dfrac{2}{3}$

2. Operations with fractions

   Find $\dfrac{2}{3} + \dfrac{3}{4}$. Give your answer as a mixed number.

   Show the answer

   Key idea: To add fractions, first write them with a common denominator.

   1. The LCD of $3$ and $4$ is $12$
   2. $\dfrac{8}{12} + \dfrac{9}{12} = \dfrac{17}{12}$
   3. $\dfrac{17}{12} = 1\frac{5}{12}$

   Answer: $1\frac{5}{12}$

3. Operations with negative fractions

   Evaluate:

   (a) $-\dfrac{2}{3} - \left(-\dfrac{5}{6}\right)$

   (b) $-\dfrac{3}{4} \times \left(-\dfrac{8}{9}\right)$

   Show the answer

   Key idea: Subtracting a negative is the same as adding its opposite. The product of two negative numbers is positive.

   1. (a) $-\dfrac{2}{3} + \dfrac{5}{6} = -\dfrac{4}{6} + \dfrac{5}{6} = \dfrac{1}{6}$
   2. (b) The signs are the same, so the answer is positive: $\dfrac{3}{4} \times \dfrac{8}{9} = \dfrac{24}{36} = \dfrac{2}{3}$

   Answer: (a) $\dfrac{1}{6}$ (b) $\dfrac{2}{3}$

4. Operations with decimals

   Find $12.6 - 4.85 + 0.375$.

   Show the answer

   Key idea: Line up the decimal points (adding zeros if needed) and work from left to right.

   1. $12.600 - 4.850 = 7.750$
   2. $7.750 + 0.375 = 8.125$

   Answer: $8.125$

5. Terminating decimals, recurring decimals and rounding

   Convert $\dfrac{9}{16}$ to a decimal and state whether it is terminating or recurring.

   Show the answer

   Key idea: If the denominator's only prime factors are 2s and 5s, the decimal terminates. Divide to find the decimal.

   1. Check the denominator: $16 = 2^4$. Only 2s, so the decimal terminates.
   2. Divide: $9 \div 16$.\

   $$\begin{aligned} 9 \div 16 &= 0.5625 \end{aligned}$$

   3. Verify: $0.5625 \times 16 = 9$ ✓

   Answer: $\dfrac{9}{16} = 0.5625$ (terminating decimal)

6. Converting fractions, decimals and percentages

   Write $\dfrac{7}{8}$ as a percentage.

   Show the answer

   Key idea: Multiply by $100\%$.

   1. $\frac{7}{8} \times 100\% = \frac{700}{8}\% = 87.5\%$

   Answer: $87.5\%$

7. Decreasing and increasing by a percentage

   A jacket has a original price of $120. It is discounted by 35%. What is the sale price?

   Show the answer

   Key idea: Multiply the original amount by the percentage kept (as a decimal).

   1. A 35% discount means the customer pays $100\% - 35\% = 65\%$ of the original price.
   2. Convert to a decimal: $65\% = 0.65$
   3. Calculate the sale price: $120 \times 0.65 = 78$

   Answer: The sale price is $78.

8. Calculating percentage change, profit and loss

   Hamid buys a second-hand bicycle for $240 and sells it for $300. Find his profit in dollars and express it as a percentage of the cost price.

   Show the answer

   Key idea: Profit = selling price − cost price. Percentage profit = $\dfrac{\text{profit}}{\text{cost price}} \times 100$.

   1. Find the profit: $300 - 240 = 60$ So the profit is $60.
   2. Express as a percentage of cost price: $\frac{60}{240} \times 100 = 25$

   Answer: Hamid makes a profit of $60, which is $25\%$ of the cost price.

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 8 integer operations worksheet
• Year 8 fractions and decimals worksheet
• Year 8 percentages worksheet
• Year 8 profit, loss and discounts worksheet