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Basic Review
Basic Review
Introduction to Ratios
A ratio is a quotient of two numbers. It is used to compare these numbers. The ratio
of a to b is written as:
Ratios are very common in everyday life. One familiar example of a ratio is miles per
gallon. If you use 4 gallons to drive 120 miles, the ratio of miles to gallons that your
car got was 120:4, or 120/4. You can then reduce this, just like you would a fraction,
to 30:1 representing 30 miles per gallon.
A ratio is a comparison of two quantities. It is interpreted as a fraction in many
applications. If the ratio compares quantities with different units, such as distance
and time units, then it is often called a rate. A percentage is a ratio in which the
second quantity is understood to be 100. That is, a percentage is a ratio that
compares a number with 100.
Setting up and Comparing Ratios
Ratios are often used to compare items. For example, when we go looking for a new
car, one criteria of comparison is the ratio "miles per gallon" the car gets, with the
most economical car getting more miles per gallon.
Before we can compare items using ratios, we need to know how to take a statement
and turn it into a ratio. When you wish to set up a ratio, you need to know:
• _The items being compared.
• _The relationship between the items.
Let's look back at the car example above. If we travel 120 miles and use 4 gallons of
gas, we want to know the ratio of miles to gallons of gas. One easy way to remember
how to set up ratios is to use the wording above "a to b." We want to determine
miles to gallons, or miles/gallons. As we saw above, this ratio is 120/4, which can be
simplified to 30/1.
