Proportion and percentage change
Use a constant rate and a percentage multiplier in everyday comparisons.
Before you begin
- Fractions and ratios
- Decimal multiplication
Recognise a proportional relationship
Two quantities are directly proportional when their ratio stays constant. If three identical notebooks cost $6, the unit price is $2 and five cost $10. The graph of cost against quantity passes through the origin. A fixed delivery charge breaks direct proportionality because zero notebooks would no longer mean zero total cost.
Apply a percentage multiplier
A percentage is a fraction out of 100. An increase of 15% keeps the original 100% and adds 15%, giving a multiplier of 1.15. A decrease of 15% keeps 85%, giving 0.85. Successive percentage changes act on successive amounts, so opposite percentages do not generally cancel.
Worked example
A $40 bag is discounted by 20%. Find the sale price.
Show the worked solution
- The buyer pays 100% − 20% = 80% of the original price.
- Write 80% as 0.80 and calculate 40 × 0.80.
- Check that the $8 reduction is one-fifth of $40.
$32.
Try it yourself
A price rises 10% and then falls 10%. What happens overall?
Common mistakes
- Always identify the amount the percentage is based on.
What can you explain now?
A $60 jacket is reduced by 15%. What is the new price?
Compare with the explanation
$51.
The remaining proportion is 0.85. Calculate 60 × 0.85 = 51; the discount is $9.
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Common Core mathematics standards ↗