Year 7 Fractions and percentages: free practice test with answers

Sample fractions and percentages questions with answers

Try each one before you open the answer.

1. Introduction to fractions

   A pizza is cut into $8$ equal slices and $3$ slices are eaten. What fraction of the pizza is eaten, and what fraction is left?

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   Key idea: The denominator is the number of equal parts in the whole; the numerator is the number of parts being counted.

   1. There are $8$ equal parts, so the denominator is $8$
   2. $3$ parts are eaten: $\dfrac{3}{8}$
   3. $8 - 3 = 5$ parts are left: $\dfrac{5}{8}$

   Answer: Eaten $\dfrac{3}{8}$, left $\dfrac{5}{8}$

2. Equivalent fractions and simplified fractions

   Write $\dfrac{35}{56}$ in simplest form.

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

   1. Factors of $35$: 1, 5, 7, 35. Factors of $56$ include $7$ ($56 = 7 \times 8$)
   2. HCF $= 7$
   3. $\dfrac{35 \div 7}{56 \div 7} = \dfrac{5}{8}$

   Answer: $\dfrac{5}{8}$

3. Ordering fractions

   Which is larger, $\dfrac{5}{8}$ or $\dfrac{3}{5}$?

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   Key idea: Write both fractions with a common denominator, then compare numerators.

   1. Lowest common denominator of $8$ and $5$ is $40$
   2. $\dfrac{5}{8} = \dfrac{25}{40}$ and $\dfrac{3}{5} = \dfrac{24}{40}$
   3. $25 > 24$, so $\dfrac{5}{8}$ is larger

   Answer: $\dfrac{5}{8}$

4. Adding fractions

   Calculate $\dfrac{2}{3} + \dfrac{3}{4}$.

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   Key idea: To add fractions with different denominators, first find a common denominator, then add the numerators.

   1. Find the lowest common denominator (LCD) of 3 and 4: $\text{LCD} = 12$
   2. Rewrite each fraction with denominator 12:\

   $$\frac{2}{3} = \frac{8}{12}, \frac{3}{4} = \frac{9}{12}$$

   3. Add the numerators:\

   $$\frac{8}{12} + \frac{9}{12} = \frac{17}{12}$$

   4. Convert to a mixed number:\

   $$\frac{17}{12} = 1\frac{5}{12}$$

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

5. Multiplying fractions

   Calculate $\dfrac{3}{4} \times \dfrac{2}{5}$.

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   Key idea: Multiply the numerators together and the denominators together, then simplify.

   1. Multiply the numerators: $3 \times 2 = 6$
   2. Multiply the denominators: $4 \times 5 = 20$
   3. Write the result: $\dfrac{6}{20}$
   4. Simplify by dividing numerator and denominator by the highest common factor of 2: $\frac{6}{20} = \frac{3}{10}$

   Answer: $\dfrac{3}{10}$

6. Dividing fractions

   Calculate $\dfrac{5}{6} \div \dfrac{2}{3}$.

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   Key idea: To divide by a fraction, keep the first fraction, change the division sign to multiplication, and flip the second fraction (use its reciprocal).

   1. Keep $\dfrac{5}{6}$, change $\div$ to $\times$, flip $\dfrac{2}{3}$ to $\dfrac{3}{2}$:\

   $$\frac{5}{6} \times \frac{3}{2}$$

   2. Simplify before multiplying: the 6 and the 3 share a common factor of 3:\

   $$\frac{5}{\cancel{6}^{\,2}} \times \frac{\cancel{3}^{\,1}}{2} = \frac{5}{2} \times \frac{1}{2} = \frac{5 \times 1}{2 \times 2}$$

   3. Multiply numerators and denominators:\

   $$\frac{5}{4}$$

   4. Convert to a mixed number:\

   $$\frac{5}{4} = 1\frac{1}{4}$$

   Answer: $1\dfrac{1}{4}$

7. Finding a percentage of a number

   Find $15\%$ of $80$.

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   Key idea: Convert the percentage to a decimal by dividing by $100$, then multiply by the quantity.

   1. Convert the percentage to a decimal: $15\% = 15 \div 100 = 0.15$
   2. Multiply by the quantity: $0.15 \times 80$
   3. Calculate: $0.15 \times 80 = 12$

   Answer: $15\%$ of $80$ is $12$.

8. Introduction to ratios

   Simplify the ratio $24 : 36$.

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   Key idea: Divide both parts of the ratio by their highest common factor (HCF).

   1. Find the HCF of $24$ and $36$: the HCF is $12$.
   2. Divide both parts by $12$:\

   $$24 : 36 = (24 \div 12) : (36 \div 12)$$

   3. Simplify:\

   $$= 2 : 3$$

   Answer: $2 : 3$

Free worksheets for this chapter

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

• Year 7 fraction operations worksheet
• Year 7 fractions and decimals worksheet
• Year 7 percentages worksheet
• Year 7 ratios worksheet