Math Skills: Fractions

Lesson 2: Lesson Two-Ratios and Proportions

Learn to do ratios and proportions, practical problems involving these.

Section One-Ratio

A ratio is a comparison of two numbers, comparing a part to a whole or a part to another part. Another name for ratio is "fraction"! Simple as that, so that when you think ratio think fraction, and when you think fraction think ratio.

There are a couple of different ways to write ratios:

1 to 2; 1 : 2, OR 1/2. When a ratio is really a fraction, it must be reduced, but that's for the next lesson.

Supposing you have a "story" or word problem that requires a ratio. If so, make sure you write the ratio in the order that is stated in the problem. For instance:

"Mike takes home $2,400 a month and pays $800 per month rent. What is the ratio of his rent to take-home pay?

Since the question is "rent to take-home pay", you have to express the rent first in the ratio.

The ratio becomes $800 to $2400, $800 : $2400, or $800/$2400 (as a fraction, 800/2400), which reduces to 1/3 or 1 : 3.

A more practical real-world application of this is when you have to find the won-lost percentage of a sports team. Supposing though you know how many games a team won and how many it lost? The thing is you need to know the percentage of games won to games played. Thus you first find the number of games played by adding games won and games lost.

Example: Mike's baseball team won 12 games and lost 8 games. What is the ratio of games won to games played (which one uses to find won-lost percentage...but that's another subject)?

Won + Lost = 12 + 8 = 20. The ratio is games won to games played, so the ratio is 12 : 20 or 12/20, which when reduced is 3/5 or 3 : 5.

Here's another application: supposing the government mandated that for every three male employees there had to be two females. The ratio is 3 : 2, but supposing a workplace had 12 male employees and six female employees. Would the workplace be in compliance?

Well, 12 : 6 does not equal 3 : 2. (It equals 2 : 1). So, how could the workplace become in compliance? Would it have to fire 3 males to make the male-to-female ratio 3 : 2 (9 : 6 = 3 : 2), or would it hire more females, and, if so, how many females would have to be hired?

That leads to the next section, proportion.

For further study you may want to read more about ratios in Cambridge GED, pages 112 and 113.

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