Two numbers may be compared by expressing the relative size as the quotient of one number divided by the other and is called a ratio. Ratios are simplified fractions written with a colon (:) instead of a division bar or slash For example, the ratio of 4 and 8 can be written as fraction 4/8 , or 4 : 8. And it reads this way: the ratio is four to eight.

Example:

Paula was bored and decided to go to Manhattan to do some shopping. She bought the following items:

6 small bottles of nails polish

4 bottles of perfume

A collection of 12 yoga books

1 bottle of water

She puts everything in a bag, and took a taxi back to her house.

1) What is the ratio of the books to bottles of perfume

The answer can be given in 2 ways:

A) As a fraction 12/4, or

B) As a ratio 12 to 4, and 12 : 4

2) What is the ratio of the nails polish to the total of items in the bag. There are 4 small bottles of nails polish, and 3 + 6 + 12 + 1 = 22 items total in the bag.

The
answer can be expressed as 4/22 , 4 to 22
or 4 : 22

Example:

Last December around Christmas, Jean paid $800 for a stereo and Ron paid $600 for the same stereo. Compare the amount that Jean paid to the amount that Ron paid, using ratios.

Solution:

Step 1: Divide the numbers to be compared. In this example
the amount paid by Ron is being compared to the amount paid by Jean. The amount
paid by Jean is divided by the amount paid by Ron = 800/600

Step 2: Simplifying this expression, both 800 and 600 can be divided by 100.

Step 3: Expressing this fraction as a ratio:

Total Jean’s price/Total Ron’s price = 8:6

Expressing this fraction as a ratio:

Jean’s price/ Ron’s price = 8/6

Therefore, the ratio is 8/6, or 8: 6

Example:

If one yard equals three feet, what is the ratio of yards to feet?

Solution:

Step 1: 1 yd./ 3 ft.

Step 2: 1/3 is already in simplest terms

Step 3: yards/feet = 1/3 or yards : feet = 1:3