Year 8 - Percentages - Free practice

Year 8 Percentages Worksheets & Practice Tests

Increases, decreases, GST, percentage error.

Quick answer

How do you solve percentage increase, decrease and error problems?

Multiply the original by (1 + r/100) to increase or (1 − r/100) to decrease, where r is the rate. For reverse problems, divide the final amount by the multiplier to find the original. Percentage error = (|measured − actual| ÷ actual) × 100. For example, a 20% increase on $50 gives $50 × 1.20 = $60.

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Worked examples

Year 8 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 increase and decrease
A jacket has a original price of $120. It is discounted by 35%. What is the sale price?
Show worked solution
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.
Example 2 · Reverse-percentage problem
After a 20% increase, the price of a concert ticket is $66. What was the original price?
Show worked solution
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.
Example 3 · Commission and mark-up in a real-life context
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 worked solution
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.

Common mistakes

Where students usually lose marks

Finding the percentage, not the new amount

35% of 120 = 42, so the sale price is $42.

The percentage change ($42) is the amount taken off, not the final price. Always subtract the discount from (or add the increase to) the original: $120 - 42 = 78$ , giving $78.

Reversing a percentage by subtracting from 100 incorrectly

Price after 20% increase is $66, so original = $66 - 20\% = 66 - 20 = 46$ .

You cannot subtract the percentage number from the dollar amount directly. Divide by the multiplier: $66 \div 1.20 = 55$ , so the original price was $55.

Applying successive percentages by adding them

A 10% increase then a 10% decrease gives 0% change overall.

Each percentage applies to a different base amount, so they do not cancel. Apply them one step at a time: after a 10% increase, $100 \times 1.10 = 110$ ; after a 10% decrease, $110 \times 0.90 = 99$ , which is a net decrease.

Calculating percentage error with the wrong denominator

$\text{Percentage error} = \dfrac{\lvert\text{measured} - \text{actual}\rvert}{\text{measured}} \times 100$

Percentage error is always calculated using the actual (true) value as the denominator: $\text{Percentage error} = \dfrac{\lvert\text{measured} - \text{actual}\rvert}{\text{actual}} \times 100\%$

Try one yourself

Your turn

A jacket is marked at $184 after a 15% increase on its original price. What was the original price of the jacket, in dollars, correct to 2 decimal places?

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About this worksheet

Why we built it

Year 8 percentages move past "percent of" into increases, decreases and percentage error - the real-life versions students will keep using. These worksheets focus on the harder applied problems where a question first needs translating before any calculation.

What's covered

Sub-skills your student will practise

✓Percentage increase and decrease
✓Reverse-percentage problems (find the original price)
✓GST (add or extract from a total)
✓Percentage error in measurement
✓Real-world problems (sales, mark-ups, commission)

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Frequently asked

Questions parents ask about percentages

What's a percentage increase or decrease?

An increase or decrease expressed as a percentage of the original. A $50 item raised to $60 is a $10 increase, which is 10/50 = 20% of the original. The formula is (change / original) x 100.

How do students do a reverse percentage problem?

If $60 is the new price after a 20% increase, divide by 1.2 to get back to the original ($50). For a 20% decrease, divide by 0.8. The 'multiplier' approach saves a lot of working.

What's percentage error?

How far off a measurement or estimate is from the true value, as a percentage. Formula: (|measured - actual| / actual) x 100. Year 8 introduces this for measurement contexts.

Is GST a Year 8 topic?

Yes - Year 8 uses 10% GST in financial contexts. Students learn both directions: adding GST (multiply by 1.1) and extracting GST from a total (divide by 1.1).

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