Ratios: Definition & Examples

A ​ratio​ is a mathematical way of comparing two quantities. The colon symbol is used to signify the ratio relationship. For example, consider a bag with 10 pieces of fruit, of which 4 are apples. The ratio of the number of apples to all the pieces of fruit can be expressed by the ratio 4:10. If you change the order of the numbers in a ratio you also change the meaning of the ratio, so the order of the numbers matters. This means 10:4 is not equivalent to 4:10.

To form a ratio, it's important to understand the relationship between the two numbers being compared. There are two basic types of ratio relationships. The first, ​part-to-whole​, compares the quantity of one type of objects to a larger group, such as the comparison of the number of apples to all the pieces of fruit. The other type of relationship is ​part-to-part​. Using the fruit example, if the bag held 4 apples and 2 bananas, then the ratio between apples and bananas can be expressed as 4:2. Notice that the total number of pieces of fruit does not enter into the part-to-part ratio.

Any ratio can be written as a fraction. To convert a ​ratio to fraction​, use the first number in the ratio as the numerator and use the second number as the denominator of the fraction. The ratio should be simplified either before or after converting to ensure the fraction is in lowest terms.

\(4:10 = \frac{4}{10} = \frac{2}{5}\)

You can also convert a fraction to a ratio by reversing the above operation.

\(\frac{1}{3} = 1:3\)

A number that is expressed as a percentage can be seen as a type of ratio since the number to the left of the percent sign is being compared to 100. You can convert a ​ratio to a percentage​ by first converting the ratio to a fraction, then dividing the numerator of the fraction by the denominator and then multiplying by 100. For example:

\(1:4 = \frac{1}{4} = 1 ÷ 4 = 0.25\)

Now multiply by 100 to turn this into a percentage:

\(0.25 × 100 = 25\%\)

To convert a percentage to a ratio, first create a fraction with 100 in the denominator. Simplify the fraction and then form the ratio by placing the numerator to the left of the ratio sign and the denominator to the right.

\(75\% = \frac{75}{100} = \frac{3}{4} = 3:4\)

For more information on ratios, watch the video below: