# Proportion

How to solve a proportion (colon form, fraction form): 2 examples and their solutions.

## ExampleColon Form. (2x + 1) : 3 = x : 2

Solution

Solution (Detail)

To solve a proportion in colon form,

set

the product of the outer numbers, (2x + 1)⋅2

and the product of the inner numbers, 3⋅x

are equal.

So (2x + 1)⋅2 = 3⋅x.

(2x + 1)⋅2 = 4x + 2

Multiply a Monomial and a Polynomial

3⋅x = 3x

Solve the equation 4x + 2 = 3x.

Then x = -2.

Linear Equation (One Variable)

So x = -2 is the answer.

## ExampleFraction Form. x/2 = (4x - 1)/5

Solution

Solution (Detail)

To solve a proportion in fraction form,

cross product the numbers:

x⋅5 = 2⋅(4x - 1).

x⋅5 = 5x

2⋅(4x - 1) = 8x - 2

Solve the equation 5x = 8x - 2.

Then x = 2/3.

So x = 2/3 is the answer.