Simplifying Ratios

Ratios are used to make comparisons between two numbers.
-  Ratios can be written as a fraction, using the word "to", or with a colon. Example: or “3 to 4” or 3:4
-  You can calculate equivalent ratios by multiplying or dividing both sides of the ratio by the same number.

Examples:
Example 1.  Simplify.
Solution: Both numbers and are divisible by ⇒ ,
, Then:

Example 2.  Simplify.
Solution: Both numbers and are divisible by ⇒ , , Then:  

Example 3.  There are 24 students in a class and 10 are girls. Find the ratio of girls to boys in that class.
Solution: Subtract from to find the number of boys in the class.
. There are boys in the class. So, the ratio of girls to boys is . Now, simplify this ratio. Both and are divisible by .
Then:, and . In the simplest form, this ratio is

Example 4.  A recipe calls for butter and sugar in the ratio . If you're using 9 cups of butter, how many cups of sugar should you use?
Solution: Since you use 9 cups of butter, or 3 times as much, you need to multiply the amount of sugar by 3. Then: . So, you need to use 12 cups of sugar. You can solve this using equivalent fractions: