 # Direct proportion for OCR A-level Maths 1. Direct proportion
2. Converting units

Two quantities are directly proportional to each other when they are multiples of each other. The notation for direct proportionality is a ∝ b. Equations can be constructed using a constant of proportionality and evaluating it using given information. To convert a value from larger units to smaller units, multiply it by the ratio between the units. To convert a value from smaller units to larger units, divide it by the ratio between the units. Sometimes a conversion of units can achieved by multiplying or/and dividing a value in steps.

1 km = 1000 m
1 m = 100 cm
1 cm = 10 mm
1 kg = 1000 g
1 hour = 60 min = 3600 s # 1

z is directly proportional to s². Given that when s = 3, z = 54, construct an equation for the relationship between z and s².

Since z is directly proportional to s², z = ks², where k is a constant of proportionality.
Substituting s = 3, z = 54 into this gives 54 = k(3²), thus k = 6.
Therefore, z = 6s².

z = 6s² # 2

x is directly proportional to y. Given that x = 10 when y = 2, construct an equation for the relationship of x and y.

Since x is directly proportional to y, x = ky, where k is a constant of proportionality.
Substituting y = 2, x =10 into this gives 10 = k × 2, therefore k = 5.
Thus, the equation is given by x = 5y.

x = 5y # 3

Convert 100 m to cm.

100 m = 100 × 100 cm = 10000 cm

10000 cm # 4

How many hours are in 72 seconds?

72 seconds = 72 ÷ 3600 hours = 0.02 hours

0.02 # 5

The density of an object is given by 1200 g/cm³. Calculate the density of the object in kg/cm³.

1200 g = 1200 ÷ 1000 kg = 1.2 kg
Therefore, the density is given by 1.2 kg/cm³

1.2 kg/cm³ End of page