Working with Proportion

Working with Proportion

Working with 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)

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 tripled'

    • The quantity is multiplied by three

  • Alternatively, find the factor by dividing the 'new' quantity by the 'old' quantity

• 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

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?

• 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

What is inverse proportion?

• Inverse proportion

  • As one quantity increases by a certain rate (factor)

  • The other quantity will decrease by the same rate

• This relationship applies vice versa too, if one quantity decreases the other increases 

• E.g. If 2 robots take 15 hours to build a car

  • Tripling the number of robots (6) would mean the time taken to build a car would be divided by 3 (5 hours)

How do I solve inverse proportion questions?

• Read through wordy inverse 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

• Find the factor that you will be increasing/decreasing by

  • This may be given to you in the question, e.g. 'the amount is tripled'

  • Alternatively, find this by dividing the 'new' quantity by the 'old' quantity

• Divide the other quantity by this factor to find the required quantity

• Give your final answer in context

  • Round and give units where appropriate

How do I use the unitary method with inverse proportion?

• This is similar to the unitary method for direct proportion

  • Just remember to do the opposite operation when scaling

• For example, 5 workers take 20 hours to complete a job, find how long it would take 8 workers

  • Find the time it would take 1 worker (1 unit)

    • The number of workers decreases

    • Therefore, the time increases

    • 5 × 20 hours = 100 hours

  • Scale this unit up to get the required number

    • The number of workers increases

    • Therefore, the time decreases

    • 100 hours ÷ 8 = 12.5 hours