Ratios, Proportions, and Percents

SAT Math Overview. Topic: Ratios, Proportions, and Percents.

Overview

Ratios, proportions, and percents cover a broad set of topics, and you need to be familiar with these topics because you will see several SAT math questions on these topics. In this section we’ll cover the following:

  • Ratios and Rates
  • Proportions
  • Percents

Let’s look at each of these in more detail:

Ratios and Rates

What is a ratio? It is a relationship between two quantities. Take a look at the definition.

Ratio .The relationship between two numbers, represented as a quotient. The numbers in the ratio must have the same units of measurement or represent similar quantities.

Click on this link to learn more about ratios. This slide show includes a video and examples of different ratios. Here are some additional ratios topics you should review. Each of the following includes a link to a slide show with additional content:

A rate is a special type of ratio. Look at this definition.

Rate. A ratio that compares two different types of quantities. The resulting unit of measurement is based on the individual quantities.

Click on this link to learn more about rates. This slide show includes a video and examples of different rates. 

Another topic related to rates is unit rates. Look at this definition.

Unit Rate. A rate expressed as a ratio with 1 in the denominator or sometimes as a decimal.

Click on this link to learn more about unit rates. This slide show includes a video and examples of different unit rates. 

SAT Skill: Ratios and Rates

Example 1

A car moves 120 ft in 5 seconds. At that speed, about how many miles will it travel in 2 hours?

This is a rate problem, so use the measurements to find the speed in ft/sec.

Calculating Speed

Now convert to miles per hour:

Converting from feet per second to miles per hour.

Now determine the distance traveled in 2 hours:

Multiplying speed by time to calculate distance traveled.

Example 2

The Wifi at a hotel costs 60 cents a minute, after an initial cost of 4.99. Write an equation that can be used to find the total cost, c, in dollars per hour h.

This is a rate problem. Take the cents per minute rate and convert it to a dollars per hour rate:

Converting cents per minute to dollars per hour.

Now you can write the equation for c:

c equals 36 h plus 4.99

Proportions

When two ratios are equal to each other, they can form an equation called a proportion. Look at this definition.

Proportion. When two ratios are equal, they form a proportion.

To learn more about proportions, click on this link. It is a presentation that goes over the proportions in more detail.

When proportions include a variable, this results in an equation that can be solved. 

Solving a Proportion When two ratios are equal to each other, you can set up and solve a proportion. There are four possible equations possible when solving a proportion.

To learn more about solving proportions, click on this link. To see worked-out examples of solving proportions, click on this link.

SAT Skill: Proportions

Example 1

A jar of peanut butter can be used to make two dozen sandwiches. How many jars of peanut butter are needed to make 240 sandwiches?

This is a proportion problem. To make 240 sandwiches requires 480 slides of bread. Here are the equivalent ratios:

1 jar is to 24 slices of bread as x jars is to 480 slices of bread.

Solve for x:

Solving the proportion x over 480 equals 1 over 24.

Percents

A percent is a ratio where the denominator is 100. You can also think of a percent as a fraction with a denominator of 100. Take a look at this definition.

Percent The fractional part out of 100. Percents can be expressed as whole numbers, decimals, and fractions.

To learn more about percents, click on this link. In working with percents, there are three different types of equations to solve. For each of the cases below, click on the link to see a slide show that provides additional content:

SAT Skill: Percents

Example 1

In a population of fish, 8% are tagged for tracking. If a total of 375 fish are released, how many of them are tagged?

We are dealing with this case:

A percent equation. Tagged fish = 8 percent of Total Fish population.

 

Example 2

5 is 12% of what number?

We are dealing with this case:

Percent equation Number A = 12% of Number B

Example 3

At a college 8% of the computer science majors were female. If there were 58 female computer science majors, what was the total number of computer science majors?

We are dealing with this case:

Percent equation Female computer science majors = 8% of Total computer science majors.

 

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