Idiot\'s Guides Basic Math and Pre-Algebra

86 Part 1: The World of Numbers

CHECK POINT

1. If the ratio of girls to boys in Math Club is 5:3, and there are 32 members of the
   club, how many boys are members?


2. The local car dealer sold 40 cars last month. The ratio of gas-powered vehicles
   to hybrids was 7:1. How many hybrids were sold?


3. The desired ratio of the red roses to white roses in a bouquet is 2:3. If the f lorist
   wants the bouquet to have a total of 20 roses, how many white roses and how
   many red roses will she need?


4. If the ratio of lions to tigers to bears at the zoo is 4:7:4, and there are 45 of these
   animals all together, how many tigers are there?


5. The ratio of red balloons to white balloons to blue balloons in the auditorium is
   21:20:9. If there are 900 balloons in the auditorium, how many are blue?

Solving Proportions

A proportion is a statement that two ratios are equal. The equation

1

3

2

6

 is an example of a

proportion. It says the ratio of 1 to 3 is the same as the ratio of 2 to 6, or, in other words, that the

fractions are equal.

When you look at the statement that two ratios are equal as a proportion, you can talk about

the four numbers that make up the proportion as the means and the extremes. It’s a little easier to

understand which numbers are means and which are extremes and why if you write the ratios

with colons, so let’s write

1

3

2

6

 as 1:3 = 2:6. The extremes are the numbers on the ends, the 1 and

the 6. They’re far out. The word mean talks about the middle, so the numbers in the middle, the

3 and the 2, are the means. When you do write it as a pair of equal fractions, it looks like this.

DEFINITION

A proportion is two equal ratios. The means of a proportion are the two middle

numbers. The extremes are the first and last numbers.

Proportions can be used to compare things. When you create a proportion, it’s important to be

consistent about the order. If you want to say that the ratio of the shortest side of the big triangle

to the shortest side of the small triangle is equal to the ratio of their longest sides, be sure that

extreme

mean

= mean

extreme