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Ratio Tables: Definition & Practice Problems

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  • 0:04 What Are Ratio Tables?
  • 1:05 Bike Ride Example
  • 2:37 Comparing Ratios
  • 4:40 Lesson Summary
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Lesson Transcript
Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

Ratio tables give you practical information that you can use to solve ratio problems. In this lesson, we define ratio tables and work through some practice problems that use them.

What are Ratio Tables?

It was a great presentation. You got to see a real heart beating and watch the simulated blood flow. Then you got an idea. What about your own blood? If your heart really works so hard to push blood through your arteries, you should be able to feel it. Asking your teacher how to find your pulse, you decided to measure and record how fast your heart was beating. You did the test several times, counting your heartbeats for different lengths of time.

Number of Beats How Long?
150 beats 2 minutes
225 beats 3 minutes
300 beats 4 minutes

Every one of those pairs of numbers represents a ratio, which is two numbers or quantities being compared (usually in fraction form, with one on the numerator and the other on the denominator). A ratio table is a structured list of equivalent (equal value) ratios that helps us understand the relationship between the ratios and the numbers. Rates, like your heartbeat, are a special kind of ratio, where the two compared numbers have different units. Let's look at some examples of ratio table problems.

Bike Ride Example

Maybe you like to ride your bike around town, and you're curious whether your speed is consistent during your various adventures. So, as you take each trip, you use a stopwatch to measure how long it takes to make the trip and your bike's odometer to measure the distance. Then, you set up a table, filling in the information you collected: where you went, distance to those various destinations (in feet), and the time it took to make the trip on your bike (in seconds).

Destination Time it takes How far it is
Grocery Store 250 seconds 5000 feet
Quick Stop 300 seconds 6000 feet
Library 1200 seconds 24,000 feet
Basketball Court 750 seconds 15,000 feet

To find out what your average speed is for each trip and to determine if it's the same for every ratio in the table, you'll divide distance by time for each trip.

5,000 feet / 250 seconds = 20 feet per second

6,000 feet / 300 seconds = 20 feet per second

24,000 / 1,200 seconds = 20 feet per second

15,000 / 750 seconds = 20 feet per second

Yup, you're consistent! You tend to travel at 20 feet per second, no matter where you go on your bike. So, assuming that's true, could you figure out how long it would take you to get to a new place? Absolutely!

If you know that your friend's house is three miles away, you could grab your calculator and do some arithmetic. There are 5,280 feet in a mile, so 3 x 5,280 means your friend's house is 15,840 feet away. Dividing by your 20 feet per second, you find that it will take you 792 seconds to get to your friend's house.

Comparing Ratios

In the last example, we had a complete table of values to work with. Now let's complete a table where some of the values are missing.

Numerator Denominator
5 3
6
15
24

Since we know that the ratios are equivalent, we can find the missing values. Take a look at Figure 1.

Figure 1: Calculating for the missing pieces
graphic ratio comparison

In Figure 1, there are letters in place to represent each value that we're missing. We'll use the ratio that's complete (5/3) to find the other values. Here's how it works:

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