Page 58 - Year 9

Proportion Maths set 1 and 2 Maths: 7 of 7

Key Concepts Examples Inverse proportion:
Direct proportion: The time taken, t, for passengers to be checked-in is inversely
Variables are directly proportional proportional to the square of the number of staff, s, working.
when the ratio is constant between g is directly proportional to the square root of h It takes 30 minutes passengers to be checked-in when 10 staff
the quantities.
When g = 18, h = 16 are working. How many staff are needed for 120 minutes?

Variables are inversely Find the possible values of h when g = 2
proportional when one quantity 1 3000
increases in proportion to the ∝ =
other decreasing. ∝ ℎ = 4.5 ℎ 2 2
When g = 2 3000

∝ is the symbol we use to show = ℎ = 2 120 = 2
that one variable is in proportion to 2 = 4.5 ℎ 3000
2
another. 18 = 16 2 30 = 2 = 120
18 = 4 = ℎ 10 2
4.5 3000 = = 25
Direct proportion: ∝
4.5 = 2
4 3000 = 25
= ℎ =
= 4.5 ℎ 9 2
Inverse proportion: ∝ 16 = 5
= ℎ
81

Key Words 1) e is directly proportional to f 2) x is inversely proportional to the square
When e = 3, f = 36 root of y.
Divide Find the value of f when e = 4 When x = 12, y = 9
Direct Find the value of x when y = 81

Inverse Multiply

Proportion Constant ANSWERS 1) f = 48 2) x = 4