Ratio

A ratio describes how many of one quantity we have relative to another. For example, in a room with 12 men and 15 women, the ratio of men to women is 12 to 15. Ratios are commonly written as a fraction, separated by a colon, or with words as we did above:

1.

2. 12:15

3. 12 to 15

We could also say that the ratio of men to the total number of people in the room is 12:27, and for women it is 15:27, and so on. The quantities in the ratio can be just about anything, but in most cases the quantities used are positive.

It is also important to remember that the order of the quantities in a ratio is important. When we say 12 men to 15 women, the 12 must come first since it is a ratio of men to women. 15:12 would be the ratio of women to men, not the ratio of men to women. Even though the quantities are the same, the ratio is different.

Ratios and proportions

Ratios can be scaled up or down. For example, if you have a cooking recipe that calls for a ratio of 4 eggs : 1 stick of butter, and you want to figure out how many eggs and sticks of butter you need to make twice the amount of whatever you're making, you can scale up the ratio by multiplying both values by a scaling factor, in this case, 2:

(4×2):(1×2) = 8:2

So you would need 8 eggs and 2 sticks of butter. You can scale down a ratio in the same manner, except that you would divide both values by the factor rather than multiply.

This essentially is the basis for the concept of a proportion. A proportion is simply a statement that two ratios are equal. In this case, the ratio 4:1 = 8:2 (they are called equivalent ratios), with the only difference being a factor of 2. Ratios and proportions are used in many other situations, not just cooking, both in everyday life as well as in math.