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Ratio and Proportion - GRE

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More Lessons for GRE Math, Math Worksheets

This lesson is part of a series of lessons for the quantitative reasoning section of the GRE revised General Test. In this lesson, we will learn:

  • Ratios
  • Proportions


A ratio is a comparison between two quantities of the same kind, for example:

There are 3 red sweets and 5 yellow sweets in the box. We can say the ratio of red sweets to yellow sweets is 3 to 5. Ratio can be written with the symbol ':' or as a fraction.

'3 to 5' can be written as '3:5' or ratio

Like fractions, ratios can be reduced to lowest terms. For example, if there are 6 red sweets and 10 yellow sweets in the box, then the ratio of the numbers of red sweets to yellow sweets is 6:10 which can be reduced to 3:5.

A three-term ratio can be used to compare three quantities, for example:

There are 5 red sweets, 15 yellow sweets and 30 blue sweets in the box

5 to 15 to 30 = 5:15:30 which can be reduced (divide by 5) to 1:3:6

The following video gives an introduction to ratio.
This video shows how to reduce or simplify ratios



A proportion is an equation relating two ratios.
For example, ratio

To solve a problem involving ratios, you can often write a proportion and solve it by cross multiplication.


If two pens cost $1.50, how many pens can you buy with $9.00?


You can buy 12 pens


If the ratio of the number of men to the number of women on a committee of 20 members is 3 to 2, how many members of the committee are women?

men : women : total = 3 : 2 : 5


There are 8 women in the committee.

The following video shows how to solve proportion problems using the cross product method.
The following video shows how to use ratios and proportions.

This video shows how to solve a proportion word problem.
Example: Arthur is typing a paper that is 390 words long. He can type 30 words in 1 minute. How long will it take him to type the paper?
This following two videos show how to solve word problems by writing and solving a proportion.
Example: A recipe has 5 cups of flour for every 2 cups of sugar. If I want to make a recipe with 8 cups of flour, how much sugar should I use?

Example: On a map two cities are 2 5.8 inches apart. If 3/8 inches on the map represent 25 miles, how far apart are the cities in miles?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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