Proportion · Grade 8
In Grade 8 you learn: inverse proportion and proportion equations.
Two quantities are in direct proportion when they grow together at the same rate: twice as many tickets cost twice as much. In inverse proportion one goes up as the other goes down: twice as many workers take half the time. The unitary method — find the value of one — solves almost every proportion problem.
Key facts
- Unitary method: find the value for 1, then multiply up.
- Direct proportion: both quantities are multiplied by the same number.
- Inverse proportion: when one is multiplied by k, the other is divided by k. Their product stays the same.
- Best buys: compare the price of one unit, such as one item or 100 g.
- Exchange rates: multiply to change into the new currency; divide to change back.
- Recipes: work out the amount per person, then multiply by the number of people.
Worked examples
Example 1
5 notebooks cost $6.50. How much do 8 cost?
Answer: $10.40
Example 2
Which is better value: 400 g of pasta for $1.20 or 1 kg for $2.75?
Answer: The 1 kg bag
Example 3
6 builders take 10 days to build a wall. How long would 4 builders take, working at the same rate?
Answer: 15 days
Example 4
A pancake recipe for 4 people uses 120 g flour, 2 eggs and 300 ml milk. You have 500 g flour, 5 eggs and 1 liter of milk. What is the largest number of people you can serve?
Answer: 10 people