Direct proportion is when two quantities change in the same way.
If you can multiply the first quantity by the same number (called a constant) to get the second quantity, they are in direct proportion.
For example, if 1 ice-cream costs $2, then 2 ice-creams will cost $4, 3 ice-creams cost $6, 4 ice-creams cost $8 and so on. You can multiply the number of ice-creams by 2 to get the cost of the ice-creams, so the number of ice-creams and the cost of ice-creams must be in direct proportion.
Other examples of direct proportion are:
- the cost of apples at $5 per kilogram
- total wages earned at $20 per hour
- amount of flour needed to make muffins (at 3 cups of flour for every 10 muffins)
- distance travelled and fuel used (assuming the car speed is the same).
Example One - Travel
A car travels 100 km in 1 hour. How far will it travel in 3 hours?
The multiplying constant is 100.
3 × 100 = 300 km
Example Two - Concrete
Four bags of cement are needed to make 1 cubic metre of concrete. How many bags are needed to make 5 cubic metres of concrete?
The multiplying constant is 4.
5 × 4 = 20 bags
Example Three - Medication
A sick child whose mass is 14 kg should receive medication dose that is in proportion to the dose of a 70 kg adult. If the adult dose is 10ml, how much should the child receive?
The multiplying constant is 70 ÷ 14 = 5.
10 ÷ 5 = 2 ml.
Q1. In adult cod fish who are constantly consuming seawater as they swim, their kidneys make urine at a constant rate of 50 millilitres every hour. How much urine does a cod fish make and excrete into the ocean in 5 hours?
Q2. Malik, a talented muffin maker, uses 2 cups of blueberries in every batch of muffins. How many cups of blueberries does he use when he bakes 6 batches?
Q3. My computer can download 100 MP3 tracks in 2 hours, how many can it download in 8 hours? (Hint: Find the multiplying constant, that is, the number of MP3s downloaded in 1 hour.)
Q4. A sick child whose mass is 28 kg receives a proportional dose to a 70 kg adult's dose of 100ml. What is the child's dosage?
Q5. In 1998, Australian Olympic gold medallist won the 200 metres freestyle in 1 minute 46.7 seconds and then the 400 metres freestyle in 3 minutes 44.35 seconds. Are these in direct proportion? (Hint: Work out the time for swimming 100 metres in each race.)
A1. 250 ml
A4. 40 ml
Did You Know That...?
Caffeine, found in coffee, tea, soft drinks and "energy drinks", can be fatal in large doses. One must consume 80 to 100 cups in a short time period. Its effect is proportional to a person's mass. One can also suffer unhealthy symptoms from too much caffeine.