Proportion

Proportion

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

Example 1: Fraction Form

Solve the given proportion. x/2 = (4x - 1)/5

A proportion is an expression
that shows
two ratios are equal:
(ratio 1) = (ratio 2).

Ratio

To solve a proportion in fraction form,
set [the products of the diagonal numbers] equal.

So x⋅5 = 2⋅(4x - 1).

This is true because
if you multiply the denominators on both sides (× 2⋅5),
you get the next line result.

Then solve the equation.

Linear equations (One variable)

Example 2: Colon Form

Solve the given proportion. (2x + 1) : 3 = x : 2

To solve a proportion in colon form,
set an equation like this:

The product of the outer numbers (blue)
is equal to
the product of the inner numbers (purple).

So (2x + 1)⋅2 = 3⋅x.

Then solve the equation.

Linear equations (One variable)

Example 3

Chocolate milk is made by mixing 2 spoons of chocolate powder with 3 cups of milk. To make the same taste, how much spoons of chocolate powder are needed for 12 cups of milk?

Before writing a proportion,
first write down the given conditions.

It's good to make a table like this.

The number of spoons of chocolate powder
is the value that you're looking for.
So set the value as x.

Write the proportion
by using the table.

To make the same taste,
the ratio of the ingredients should be
(2 spoons)/(3 cups).

So 2/3 = x/12.

Ratio

Solve the proportion
by setting
[the products of the diagonal numbers] equal.

So 3⋅x = 2⋅12.

Divide both sides by 3.

Then x = 8.

So 8 spoons of chocolate powder are needed
for 12 cups of milk.

Linear equations (One variable) - Example 3