Year 8
Direct
Proportion
Learning Objective
Solve direct proportion problems using
unitary and multiplicative methods
What is Direct Proportion?
Direct proportion is a
correlation between
two variables in which
an increase in one
variable results in a
proportionate increase
in the other variable.
Direct Proportion Graph
Real-life Examples
Some simple examples of directly proportional relationships include:
The more hours worked, the higher the earnings
Purchasing more of a particular item results in a higher cost
Preparing larger quantities of food requires more ingredients
Decide which are in direct proportion…
The amount of paint required
and the size of a wall
The time taken to complete a job
when there are more workers
A buffet meal's total cost based
on the number of people
The distance travelled and the
amount of time it takes
Decide which are in direct proportion…
The amount of paint required
and the size of a wall
The time taken to complete a job
when there are more workers
A buffet meal's total cost based
on the number of people
The distance travelled and the
amount of time it takes
Inverse Proportion
This is an example of inverse proportion as one
variable increases, the other decreases
The time taken to complete a job
when there are more workers
More workers = Less time taken
Example
Donna needs 180g of flour to bake a batch of 12 cookies. How
much flour would she need to make 38 cookies?
x3
12 cookies:
180 g flour
36 cookies:
540 g flour
x3
This is known as a multiplicative method as you
can scale up by multiplying
Example
Timothy earns £45 for working 3 hours. How much
would he earn if he worked 5 hours?
1 hour:
£45 ÷ 3 = £15
5 hours:
£15 x 5 = £75
Calculating the price of 1 unit is known at the unitary method
Example
8 croissants cost £9.60.
How much would 5 croissants cost?
1 croissant:
£9.60 ÷ 8 = £1.20
5 croissants:
£1.20 x 5 = £6
Practice
1. Samira buys 4 pens for 60p.
a. How much does 1 pen cost?
b. How much would 9 pens cost?
2. Chad works for 6 hours and gets paid £108.
a. What is his hourly rate of pay?
b. How much does he get paid for 9 hours of work?
3. A batch of 12 cupcakes requires 90g of sugar. Aaron wants to make a large
batch for a party. How much sugar does he need for 60 cupcakes?
Answers
1. Samira buys 4 pens for 60p.
a. How much does 1 pen cost?
b. How much would 9 pens cost?
1 pen = 15 p
9 pens = £1.35
2. Chad works for 6 hours and gets paid £108.
a. What is his hourly rate of pay?
b. How much does he get paid for 9 hours of work?
£18/hour
£162
3. A batch of 12 cupcakes requires 90g of sugar. Aaron wants to make a large
batch for a party. How much sugar does he need for 60 cupcakes?
450 g
Any
Questions?