Two variables are proportional if their ratio is constant. The constant is named a constant of proportionality.

Given that the two variables x and y are proportional to each other, a simple way to express the proportionality is shown below.

(Note: "α" means "is proportional to").

y α x    (or  x α y)

The way this proportionality is usually expressed in mathematics is shown below.

y = kx    (or  x = cy)

y = kx (where k is the constant of proportionality).

k and c are each constants of proportionality. c and k are always reciprocals of each other and are calculated using two known related values of each variable, as shown below.

Since 100 cm is equivalent to 1 m, how many metres are equivalent to 57.3 cm and how many centimetres are equivalnet to 31.5 m?

y: length in metres

x: length in centimetres

How many metres are equivalent to 57.3 cm?

y = kx    (Since the unknown is metres use y = kx rather than x = cy.)

0.573 m are equivalent to 57.3 cm.

How many centimetres are equivalnet to 31.5 m?

y = kx    (Since the unknown is metres use y = kx rather than x = cy.)

3150 cm are equivalent to 31.5 m.

Only one of the two "formulas" is needed to solve both types of problems, and often units are not displayed till the final result.

So if we know the following:

y: length in metres

x: length in centimetres

x = 100y

How many metres are equivalent to 57.3 cm?

57.3 = 100y

0.573 = y

0.573 m are equivalent to 57.3 cm.

How many centimetres are equivalnet to 31.5 m?

x = 100(31.5)

x = 3150

3150 cm are equivalent to 31.5 m.