Rates Are Ratios

Rates and ratios can be difficult concepts. Rather than trying to master several small topics, you're more likely to conquer the subject by treating as one large one.

Rates, ratios, percents, and even fractions are all roughly the same idea. (That's why one of my problem sets focuses specifically on rates, ratios, and percents.) That idea: The relationship between two quantities.

Think about a school with a certain number of students and teachers. We could express the relationship between the number of students and the number of teachers in several ways:

• The fraction of people at the school who are teachers
• The percent of people at the school who are students
• The student-teacher ratio
• The rate at which the school hired teachers for a given number of students

Also consider some common rates, and how they could be expressed as ratios:

• Miles per hour = the ratio of number of miles to number of hours
• Acceptance rate = the ratio of number of accepted students to total applicants

The key point here is that these are all fractions. Whether or not you see the specific words "per" or "rate," you are looking for relationships between quantities.

This concept of "relationships" stretches even further. An average is the relationship between some total and a number of items. A probability is the relationship between the number of desirable outcomes and the number of positive outcomes. The list goes on.

All of these relationships are, at their core, the same concept. Rather than focusing on the minutia of individual problems and specific topics, look for commonalities. There are lots of rates, ratios, percents and fractions on the GMAT, so you'll have plenty of chances to practice.

About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

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