List of Notes - Category: Ratios and Proportions


A ratio is a comparison of two numbers by division.

The ratio of `m` to `n` can be expressed in the following ways:

  • `m` to `n`
  • `m:n`
  • `m/n`

Last expression tells us, that ratio is, actually, a fraction.


An equation, stating that two ratios are equal is called a proportion.

For example, `5/3=10/6` is a proportion.

Example 1. Determine, whether the ratios `18/4` and `27/6` form a proportion.

Let's reduce first ratio: `18/4=(9*color(red)(2))/(2*color(red)(2))=9/2`.

Solving Percent Problems

Basically, there are 3 types of percent problems:

  • What is `p`% of `m`?
  • `p`% of what is `m`?
  • What percent of `m` is `n`?

Now, we will practice in these percent problems.

These types of problems can be easily solved using proportions.