Direct Proportion
What is direct proportion?
- Direct proportion
- As one quantity increases/decreases by a certain rate (factor)
- The other quantity will increase/decrease by the same rate
- The ratio of the two quantities is constant
- E.g., 2 boxes of cereal is 800 g of cornflakes
Doubling the number of boxes of cereal (4 boxes) will double the amount of cornflakes (1600 g)
- E.g., 2 boxes of cereal is 800 g of cornflakes
How do I solve direct proportion questions?
- Read through wordy direct proportion questions carefully
- Ensure that you understand the context of the question
- Some questions may tell you the relationship between the two values as a ratio
- Identify the two quantities involved
- E.g. Hours worked and pay
- Find the factor that you will be increasing/decreasing by
- This may be given to you in the question, e.g., 'the amount is doubled'
- E.g. Three times as many hours are worked
- Alternatively, find this by dividing the 'new' quantity by the 'old' quantity
- This may be given to you in the question, e.g., 'the amount is doubled'
- Multiply the other quantity by this factor to find the required quantity
- E.g. If three times as many hours are worked, the pay will be three times more in total
- Give your final answer in context
- Round and give units where appropriate
What is the unitary method?
- The unitary method means finding one of something (1 unit of something)
- This can be a useful strategy
- For example, find the weight of 7 boxes if 8 boxes weigh 60 kg
- Find the weight of 1 box (1 unit) using division
- 60 kg ÷ 8 boxes = 7.5 kg per box
- Scale this unit up using multiplication
- 7.5 kg per box × 7 boxes = 52.5 kg
- Find the weight of 1 box (1 unit) using division
How do I find which item is the best value?
- A common proportion question is to find which product is the best value for money
- Which is best value for money?
- 1.5 kg of flour for $0.84
- or 5 kg of flour for $2.65?
- Which is best value for money?
- To do this, compare the prices of 1 kg (1 unit):
- Divide the price in dollars by the weight this buys
- $0.84 ÷ 1.5 kg = $0.56 per kg
- $2.65 ÷ 5 kg = $0.53 per kg
- Make sure you compare prices for the same size unit of both items
- The lowest unit price is the best value (0.53 < 0.56)
- 5 kg of flour for $2.65 is better value for money than 1.5 kg of flour for $0.84
- Divide the price in dollars by the weight this buys
Examiner Tip
- Start a question by jotting down the key values involved.
- You'll be able to pick them out quickly and easily later on.
Worked example
The bonus received by an employee is directly proportional to the profit made by the company they work for.
Bonuses are paid at a rate of $250 per $3000 profit the company makes.
Work out the bonus an employee receives if the company makes a profit of $18 000.
Identify the two quantities 'profit' and 'bonus'
Find the factor ('new' ÷ 'old') from the profit
Multiply the bonus by the factor
Answer in context with units
An employee should receive a bonus of $1500
We are still working with profit and bonus
Find the factor using 'new' ÷ 'old'
Find the amount of bonus by multiplying by the factor
Answer in context with units
The lowest amount of bonus an employee could receive is $50