An equation that tells us that one ratio is equal to another ratio is called a
A baseball team wins 15 games out of 30 games played. If the team continues
to win at the same rate, how many games will it win out of 40 games played?
a. Let N = number of games the team will win in 40 games played.
b. The ratio of games won to games already played is 15/30. Since the ratio of
games won to games played is to remain the same, we may write this ratio as N/40.
These ratios may also be written as 15:30 and N:40.
We may now write the equation 15/30 = N/40. This is our proportion.
1-55. PROPERTY OF PROPORTIONS
Proportions have a very useful property. Consider the proportion: 3 = 6 or 1:3 =2:6.
a. The two inside terms (3 and 2) are called the "means" of the proportion, and
the two outside terms (1 and 6) are called the "extremes" of the proportion.
b. Notice that if we multiply the two means, we obtain 3 x 2 = 6. Also, if we
multiply the two extremes, we obtain 1 x 6 = 6. This illustrates the following property of
**In a proportion, the product of the means is equal to the product of the extremes.**
EXAMPLE: The ratio of alcohol to water in a certain type of antifreeze is
3:4. If a tank contains 24 quarts of alcohol, how many quarts of
water must be added to make the antifreeze mixture?
Let X = the number of quarts needed.
3 = 24