# Proportion

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

## Example 1: Fraction Form

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⋅(4*x* - 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

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 (2*x* + 1)⋅2 = 3⋅*x*.

Then solve the equation.

Linear equations (One variable)

## Example 3

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