Year 7 - Percentages - Free practice

Year 7 Percentages Worksheets & Practice Tests

Discounts, GST, percent of a number - the financial-maths backbone.

Quick answer

How do you find a percentage of a quantity?

Convert the percentage to a decimal or fraction, then multiply by the quantity. For example, 15% of 80 = 0.15 × 80 = 12. To express one quantity as a percentage of another, divide the part by the whole and multiply by 100. For example, 18 out of 24 = (18 ÷ 24) × 100 = 75%.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 7 percentages: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Percentage of a quantity
Find $15\%$ of $80$ .
Show worked solution
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 $12$ .
Example 2 · Expressing one quantity as a percentage of another
A student scored $36$ out of $48$ on a maths test. Express the student's score as a percentage of the total, rounded to one decimal place.
Show worked solution
Key idea: Write the score as a fraction of the total, then multiply by $100$ to convert to a percentage.
1. Write as a fraction: $\dfrac{36}{48}$
2. Multiply by $100$ : $\frac{36}{48} \times 100$
3. Simplify the fraction first: $\dfrac{36}{48} = 0.75$
4. Calculate: $0.75 \times 100 = 75$
Answer: The student scored $75\%$ .
Example 3 · Discount word problem
A pair of sneakers is priced at $120. A shop is offering a $25\%$ discount. How much does a customer pay after the discount?
Show worked solution
Key idea: Find the discount amount by calculating the percentage of the original price, then subtract it from the original price.
1. Find the discount amount: $25\%$ of $120
2. Convert to a decimal: $25\% = 0.25$
3. Calculate the discount: $0.25 \times 120 = 30$
4. Subtract the discount from the original price: $120 - 30 = 90$
Answer: The customer pays $90.

Common mistakes

Where students usually lose marks

Dividing instead of multiplying after converting

15% of 80: $80 \div 0.15 = 533.3\ldots$

Once you have converted the percentage to a decimal, you multiply the decimal by the quantity. Division goes the other way and gives a much larger number, which should be a clue something is wrong. Always ask: is my answer smaller than what I started with? For a percentage less than $100\%$ , it should be.

Forgetting to subtract the discount

25% discount on $120: answer is $30

$30 is the discount amount, not the sale price. You must subtract the discount from the original price: $120 - 30 = 90$ , so the customer pays $90. Read the question carefully to check whether it asks for the discount amount or the final price.

Flipping the fraction when expressing one quantity as a percentage of another

36 out of 48: $\dfrac{48}{36} \times 100 = 133.3\ldots\%$

The part always goes on top (numerator) and the total always goes on the bottom (denominator). Write the fraction as $\dfrac{\text{part}}{\text{total}}$ , which here is $\dfrac{36}{48}$ , not the other way around. A percentage over $100\%$ would mean the student scored more than the maximum, which is impossible here.

Treating percent as a whole number in calculations

$15\%$ of $80 = 15 \times 80 = 1200$

The symbol $\%$ means 'out of $100$ ', so you must divide by $100$ before multiplying. Convert $15\%$ to $0.15$ (or the fraction $\dfrac{15}{100}$ ) first. A result of $1200$ is far larger than the original quantity of $80$ , which is a clear sign the conversion step was missed.

Try one yourself

Your turn

A jacket has a marked price of $140. It is discounted by 35%. What is the sale price of the jacket, in dollars?

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About this worksheet

Why we built it

Percentages are one of the most useful Year 7 topics for everyday life: discounts, GST, tips, mark-ups. These worksheets practise both directions - finding a percentage of a quantity, and working out what percentage one number is of another - in contexts students actually run into.

What's covered

Sub-skills your student will practise

✓Percent of a quantity (15% of 80)
✓Expressing one quantity as a percentage of another
✓Converting between fractions, decimals and percentages
✓Discount and mark-up word problems
✓Best-buy and value-for-money comparisons

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Frequently asked

Questions parents ask about percentages

What's the easiest way to find a percentage of a quantity?

Convert the percentage to a decimal (10% = 0.1, 25% = 0.25), then multiply. For 15% of 80: 0.15 x 80 = 12. This works without a calculator once the decimal-equivalents become automatic.

What kinds of percentage problems does Year 7 cover?

Year 7 covers finding a percentage of a quantity (15% of 80) and expressing one quantity as a percentage of another (15 is what percent of 60?). Percentage increase, decrease, and error are Year 8 topics.

Do students need to know percent conversions by heart?

The common ones, yes - 10%, 20%, 25%, 50%, 75% all come up so often that students should know them as decimals and fractions without thinking. The rest can be derived from those.

How are percentage word problems different from the calculations?

Word problems hide the operation. 'The shirt was $80, now $60' means students have to recognise that the discount is $20, which is 25% of $80. The translation step is where most marks are lost.

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