Percent Increase And Decrease In Everyday Australian Maths

Percentages describe how much a quantity changes compared with its original value. A price that rises from $80 to $92 has increased by $12, but the useful comparison is that $12 represents 15% of the original $80. This distinction helps with shopping, budgeting, wages, business figures and school mathematics.

A decrease works the same way. If a $250 bicycle is reduced to $200, the saving is $50, and $50 is 20% of the starting price. The final amount is therefore 80% of the original price. Keeping the original value in view prevents one of the most common percentage errors.

Australian students encounter these calculations in Australian dollars, supermarket catalogues, fuel pricing and online sales. The examples below show how to calculate a percentage change, interpret the result and recognise when two changes should not simply be added together.

Finding The Percentage Increase

To calculate an increase, subtract the original amount from the new amount. Divide that difference by the original amount, then multiply by 100:

Percentage increase = (increase ÷ original amount) × 100

Suppose a weekly grocery bill in Brisbane rises from $150 to $168. The increase is $18. Since $18 ÷ $150 = 0.12, the bill has risen by 12%. The new cost can also be found directly by multiplying $150 by 1.12, giving $168.

The original value is always the denominator in this calculation. If a café in Melbourne increases the price of a sandwich from $10 to $11.50, the change is $1.50. Dividing $1.50 by $10 gives 0.15, so the increase is 15%. Using $11.50 as the denominator would answer a different question about the change relative to the final price.

Calculating A Percentage Decrease

For a reduction, find the difference between the original and new amounts, divide by the original amount, and express the result as a percentage:

Percentage decrease = (decrease ÷ original amount) × 100

A Sydney gym membership falling from $60 per week to $51 has decreased by $9. Because $9 ÷ $60 = 0.15, the decrease is 15%. The remaining price is 85% of the original amount, so $60 × 0.85 also produces $51.

Discount labels often make this process quicker. A 30% reduction on a $120 jacket means the discount is $36, leaving a sale price of $84. In Australia, a retailer may display a recommended retail price beside a sale price, but the mathematical percentage should be checked against the stated original price and the terms of the offer.

Applying Changes To Australian Prices

Goods and services tax, or GST, adds another practical layer to price calculations. Most taxable goods and services in Australia include 10% GST in the advertised final price. If a business lists a pre-GST service at $400, the GST-inclusive amount is $400 × 1.10 = $440. Removing GST from $440 requires division by 1.10, producing $400, rather than subtracting 10% from $440.

Fuel prices provide another familiar example. If petrol rises from $1.80 to $1.98 per litre, the increase is 18 cents. The percentage change is $0.18 ÷ $1.80 × 100 = 10%. A driver buying 45 litres would pay $8.10 more for that tank, so percentage change and actual dollar impact are both worth reporting.

When checking an online promotion, calculate the percentage from the original price before applying GST, delivery charges or additional fees. A $200 item discounted by 15% costs $170 before any separate charge. Comparing the final checkout total with the advertised price gives a more accurate picture of the actual saving.

Repeated Percentage Changes

Two successive percentage changes do not usually cancel each other. Imagine a laptop priced at $1,000 receives a 20% discount and later rises by 20%. The discount gives $800, and a 20% increase on $800 adds $160, producing $960. The final price is 4% below the starting price.

The reason is that the second percentage uses a different base. The first change uses $1,000, while the second uses $800. For repeated increases, multiply by a growth factor such as 1.05 for 5%; for repeated decreases, use a factor such as 0.92 for 8%.

This idea is useful for savings, rent, inflation and investment calculations. A $500 account balance growing by 3% for two years becomes $500 × 1.03 × 1.03, or $530.45. Rounding too early can slightly alter the answer, so keep several decimal places until the final step.

Checking Reasonableness And Avoiding Errors

Estimate before calculating exactly. A rise from $250 to about $275 should be close to 10%, because $25 is one-tenth of $250. If a calculator reports 100%, inspect the subtraction, decimal placement and denominator. Percentages are ratios, so the unit often disappears during the division, but the original quantity must remain clear.

A common mistake is confusing percentage points with percentage change. If a survey result moves from 40% to 50%, it has increased by 10 percentage points. Relative to the original 40%, however, the increase is 10 ÷ 40 × 100 = 25%. These statements describe different comparisons.

Another error occurs when a discount is calculated from the wrong amount. A $50 voucher applied to a $250 purchase represents 20%, but the same voucher applied to a $400 purchase represents 12.5%. Write down the base amount beside each calculation before entering figures into a calculator or spreadsheet.

Connecting Percentages With Algebra

Percentage problems become easier when represented with equations. If an amount increases by 18%, the new value is 1.18x, where x is the original amount. If it decreases by 35%, the new value is 0.65x. This algebraic form helps solve unknown-price questions.

For example, an Australian retailer sells a desk after a 25% discount for $180. The sale price is 75% of the original, so 0.75x = 180. Dividing by 0.75 gives x = 240, meaning the original price was $240. The discount was $60.

Students who are comfortable rearranging formulas can connect percentage work with broader coordinate and algebra skills, including parallel and perpendicular lines. The same habit applies in both topics: identify the known values, choose a relationship, substitute carefully and check whether the result makes sense.

Percentage reasoning also supports interpreting test results, sales reports and mathematical competitions. Practice resources such as this problem-solving review can help students compare methods rather than relying on a single memorised rule.

For a reliable routine, write the original amount, the new amount and their difference in three lines. Then divide the difference by the original amount, multiply by 100, and verify the answer with a multiplier such as 1.12 or 0.85. Apply that routine to one real receipt or household price change today.