A shirt is reduced from $64 to $52. Find the percentage decrease.

12/64 × 100% = 18.75% decrease

Free worksheet · Australian Curriculum

Percentage worksheets with answers

Percentages turn up in discounts, test marks and price rises. Learn the four core question types with a worked example of each, then make a free worksheet with full solutions.

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Percentages at each year level, matched to the textbook chapters most Victorian schools use: a free printable worksheet with answers, sample questions, and an auto-marked test teachers can share.

Free Year 7 percentages worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

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Year 7 topics covered

Fractions and percentages
Finding a percentage of a number
Connecting decimals and percentages

Sample Year 7 percentages questions

Fractions and percentages
(a) Write $\dfrac{7}{20}$ as a percentage.

(b) Write $45\%$ as a fraction in simplest form.
Show the answer
Key idea: Percent means out of $100$ .
1. (a) $\dfrac{7}{20} = \dfrac{7 \times 5}{20 \times 5} = \dfrac{35}{100} = 35\%$
2. (b) $45\% = \dfrac{45}{100} = \dfrac{45 \div 5}{100 \div 5} = \dfrac{9}{20}$
Answer: (a) $35\%$ (b) $\dfrac{9}{20}$
Finding a percentage of a number
Find $15\%$ of $80$ .
Show the answer
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 $12$ .
Connecting decimals and percentages
Write each decimal as a percentage: (a) $0.47$ (b) $0.6$ (c) $1.25$
Show the answer
Key idea: To change a decimal to a percentage, multiply by $100$ .
1. (a) $0.47 \times 100 = 47\%$
2. (b) $0.6 \times 100 = 60\%$
3. (c) $1.25 \times 100 = 125\%$
Answer: (a) $47\%$ (b) $60\%$ (c) $125\%$
Fractions and percentages
Write $\dfrac{7}{25}$ as a percentage.
Show the answer
Key idea: Make the denominator $100$ .
1. $\frac{7}{25} = \frac{28}{100}$
2. $\frac{28}{100} = 28\%$
Answer: $28\%$

Free Year 8 percentages worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

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Auto-marked test for your class

Teachers: share one link and every student is marked straight away, with worked solutions.

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Printable practice exam

Mix in harder questions, with marks and a suggested time.

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Year 8 topics covered

Finding a percentage and expressing as a percentage
Decreasing and increasing by a percentage
Calculating percentage change, profit and loss
Solving percentage problems using the unitary method

Sample Year 8 percentages questions

Finding a percentage and expressing as a percentage
Priya sells cars and earns a 4% commission on every sale, plus a weekly base pay of $320. In one week she sells a car for $18 500 and a car for $7 250. How much does Priya earn that week in total?
Show the answer
Key idea: Commission is a percentage of the total sales value. Add base pay separately.
1. Find total sales: $18\,500 + 7\,250 = 25\,750$
2. Calculate 4% commission on total sales: $25\,750 \times 0.04 = 1\,030$
3. Add base pay: $1\,030 + 320 = 1\,350$
Answer: Priya earns $1 350 that week.
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.
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.
Solving percentage problems using the unitary method
After a 20% increase, the price of a concert ticket is $66. What was the original price?
Show the answer
Key idea: After a 20% increase, the new price equals 120% of the original. Divide by 1.20 to reverse this.
1. A 20% increase means the new price is $100\% + 20\% = 120\%$ of the original.
2. Write an equation, letting $p$ be the original price in dollars: $p \times 1.20 = 66$
3. Solve for $p$ : $p = 66 \div 1.20 = 55$
4. Check: $55 \times 1.20 = 66$ ✓
Answer: The original price was $55.

Topic guide

Percentages, explained

Most percentage questions are one of four types. Spot the type and the method follows.

1. A percentage of an amount

Change the percentage to a decimal and multiply. To find $15\%$ of $80$ :

$0.15 \times 80 = 12$

Without a calculator, build it from easy parts: $10\%$ of $80$ is $8$ , $5\%$ is $4$ , so $15\%$ is $8 + 4 = 12$ .

2. One quantity as a percentage of another

Write a fraction of the part over the whole, then multiply by $100\%$ . Scoring $18$ out of $24$ :

$\frac{18}{24} \times 100\% = 75\%$

The two quantities must be in the same units. For $45$ cents as a percentage of $3, use $300$ cents: $\frac{45}{300} \times 100\% = 15\%$ .

3. Percentage increase

To increase by $15\%$ , the new amount is $100\% + 15\% = 115\%$ of the old one. Increase $80 by $15\%$ :

$80 \times 1.15 = 92$

The new price is $92. You can also find $15\%$ of $80$ , which is $12$ , and add it on.

4. Percentage decrease

To decrease by $30\%$ , the new amount is $100\% - 30\% = 70\%$ of the old one. A $250 jacket is $30\%$ off:

$250 \times 0.7 = 175$

The sale price is $175.

5. Percentage change

Divide the change by the original amount, then multiply by $100\%$ :

$\text{percentage change} = \frac{\text{change}}{\text{original}} \times 100\%$

From $40$ to $50$ : $\frac{10}{40} \times 100\% = 25\%$ increase. From $80$ to $68$ : $\frac{12}{80} \times 100\% = 15\%$ decrease. Always divide by the original amount, not the new one.

6. Two changes in a row

Percentage changes do not simply add or cancel. A $100 price rises by $20\%$ , then falls by $20\%$ :

$100 \times 1.2 = 120, 120 \times 0.8 = 96$

It ends at $96, not $100, because the second $20\%$ is taken from a larger amount.

Quick check: 10 questions

Try each one, then open the answer.

Find $10\%$ of $70$ .
Answer
$7$
Find $25\%$ of $64$ .
Answer
$16$
Find $12\%$ of $350$ .
Answer
$42$
Find $17.5\%$ of $240$ .
Answer
$42$
Write $27$ as a percentage of $36$ .
Answer
$\frac{27}{36} \times 100\% = 75\%$
Write $40$ cm as a percentage of $2$ m.
Answer
$\frac{40}{200} \times 100\% = 20\%$
Increase $60$ by $35\%$ .
Answer
$60 \times 1.35 = 81$
Decrease $480 by $15\%$ .
Answer
$480 \times 0.85 = 408$ , so $408
A number changes from $125$ to $150$ . Find the percentage change.
Answer
$\frac{25}{125} \times 100\% = 20\%$ increase
A shirt is reduced from $64 to $52. Find the percentage decrease.
Answer
$\frac{12}{64} \times 100\% = 18.75\%$ decrease

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetPercentages Year 8 worksheetPercentages Year 8 worksheetProfit, loss and discounts Year 9 worksheetSimple interest

Questions

How do you find a percentage of an amount?

Change the percentage to a decimal and multiply it by the amount. For example, 15% of 80 is 0.15 times 80, which is 12.

How do you work out percentage change?

Find the difference between the new and original amounts, divide it by the original amount, then multiply by 100. If the amount went up it is an increase, and if it went down it is a decrease.

Do the percentage worksheets come with answers?

Yes. Every question on a generated worksheet has a fully worked solution, so students can check their method as well as the final answer.

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