Ratios and Rates
Objective Learn the concepts of ratios and
rates, and how to use them in calculations.
In this lesson, you will be introduced to ratios and rates. It
is important that you learn the meanings of these concepts.
Besides solidifying your understanding of these two concepts,
practice in calculating ratios and rates will reinforce your
multiplication and division skills.
Ratios
A ratio is a way of comparing two numbers.
Take a look at the following examples.
• The ratio of 1 to 2 is equivalent to the ratios 3 to 6
and 120 to 240.
• The ratio of 2 to 3 is equivalent to the ratios 8 to 12
and 160 to 240.
• The ratio of 5 to 3 is equivalent to the ratios 15 to 9
and 200 to 120.
The ratio of a to b can be expressed in several ways: a to b,
a : b, a out of b, and 
.
A ratio is usually written as a fraction in simplest form.
It is important that you become comfortable calculating
ratios. This will reinforce your skills with fractions. Many
times it is useful to express a ratio as a fraction in simplest
form.
Rates
A rate is the ratio of two measurements that
have different units. Rates are usually expressed in per unit
form, which is a fraction whose denominator is 1.
Be careful when dealing with measurements that have units
since they can be confusing.
Try to think about the difference between ratios and rates. It
is crucial that you understand that a ratio is simply the
quotient of two numbers, while a rate is the ratio of two
measurements that have different units (like miles and hours, or
dollars and ounces). A rate is usually expressed in per unit
form, where the denominator is 1.