Ratio Tables

A ratio table is an organized list of equivalent ratios, all representing the same relationship between two quantities. Ratio tables are a powerful problem-solving tool because they let you scale a ratio up or down to find missing values quickly. This skill is tested frequently on the GED, especially in proportion and rate problems.

What Is a Ratio Table?

A ratio table is a two-row (or two-column) chart where each pair of values maintains the same ratio. Every column in the table represents an equivalent version of the original ratio, found by multiplying or dividing both parts of the ratio by the same number.

For example, if the ratio of apples to oranges is \(\color{blue}{2 : 3}\), the ratio table looks like:

Each row is a multiple of the original ratio \(\color{blue}{2 : 3}\).

How to Build a Ratio Table

Step 1: Identify the original ratio

Find the two quantities and their ratio from the problem.

Step 2: Multiply (or divide) both parts by the same number

Each row is formed by multiplying both values in the previous row by a constant factor (or by dividing to scale down).

Step 3: Fill in missing values

If one value in a row is given, use the ratio to find the other. Divide the known value by its counterpart in a known row to find the scale factor, then multiply the other known value by the same scale factor.

Step-by-Step Summary

1. Write the original ratio as the first row of the table.
2. Choose a multiplier (1, 2, 3, …) and multiply both values to create each new row.
3. To find a missing value: identify the scale factor between a known and an unknown row, then apply it.
4. Check: every row must simplify to the same original ratio.

Watch: Solving Ratio Problems with Tables (Video Lesson)

Khan Academy demonstrates how to use a ratio table to solve ratio problems:

Worked Examples

Example 1: A car travels 60 miles per hour. Build a ratio table for hours and miles up to 5 hours.

Example 2: Complete the ratio table where the ratio of cups of water to cups of concentrate is \(\color{blue}{4 : 1}\).

To get from 4 to 20, multiply by 5; so \(\color{blue}{\text{ concentrate } = 1 \times 5 = 5}\).

Example 3: A ratio table shows: (3, 12), (?, 20), (10, ?). The ratio is \(\color{blue}{3 : 12 = 1 : 4}\). Find the missing values.

For (?, 20): \(\color{blue}{20 \div 4 = 5}\). Missing value: 5.

For (10, ?): \(\color{blue}{10 \times 4 = 40}\). Missing value: 40.

Example 4: A recipe calls for 2 eggs for every 3 cups of flour. How many eggs are needed for 15 cups of flour?

Ratio: \(\color{blue}{2 : 3}\). Scale factor: \(\color{blue}{15 \div 3 = 5}\). Eggs: \(\color{blue}{2 \times 5 = 10}\).

More Practice: Ratio Tables Example 2 Video

This follow-up Khan Academy video works through a word problem using ratio tables:

Exercises

1. The ratio of red to blue beads is \(\color{blue}{3 : 5}\). Complete the table for 3, 6, 9, 12, and 15 red beads.
2. A car gets 35 miles per gallon. How many miles can it travel on 8 gallons? Use a ratio table.
3. A ratio table for cats to dogs shows: (4, 6), (8, 12), (?, 24). What is the missing number?
4. A solution needs 5 mL of acid for every 20 mL of water. How much acid is needed for 60 mL of water?
5. A map scale shows 1 \(\color{blue}{\text{ inch } = 25}\) miles. How many miles does 7 inches represent? Use a ratio table.

Answers

1. Red	Blue
   3	5
   6	10
   9	15
   12	20
   15	25

2. Scale: 8 \(\color{blue}{\text{ gallons } \times 35}\) = \(\color{blue}{280 \text{ miles }}\).
3. Ratio is \(\color{blue}{4 : 6 = 2 : 3}\). For 24 dogs: \(\color{blue}{24 \div 3 \times 2 = 16}\) cats.
4. Ratio: \(\color{blue}{5 : 20 = 1 : 4}\). Scale factor for 60 mL water: \(\color{blue}{60 \div 20 = 3}\). Acid: \(\color{blue}{5 \times 3 = 15}\) mL.
5. Scale factor: \(\color{blue}{7 \times 25 = 175}\) miles.

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Frequently Asked Questions

What is a ratio table in math?

A ratio table is a two-row or two-column chart where every pair of values shows the same ratio. If a smoothie uses 2 bananas for every 3 cups of milk, the table might list 2 and 3, 4 and 6, 6 and 9, and 8 and 12. Each pair is an equivalent ratio, so the table helps you scale a recipe or solve a proportion.

How do ratio tables work?

Each new pair is made by multiplying or dividing both values in a known pair by the same number. Starting from 5 pages read in 2 days, doubling gives 10 pages in 4 days and tripling gives 15 pages in 6 days. Because both values always change by the same factor, the relationship between them never changes.

How do you complete ratio tables?

Find the scale factor from a column where you know one value, then apply it to the other value. Suppose a table starts with 4 tickets costing $18 and the next column shows 12 tickets with the cost missing. Since 12 ÷ 4 = 3, multiply $18 by 3 to get $54. You can also find the unit rate, $4.50 per ticket, and multiply.

How do you make a ratio table?

Write the two quantities as headings, put the original ratio in the first column, and then add columns by multiplying or dividing both numbers by the same factor. For 3 laps in 10 minutes, you could add 6 laps in 20 minutes, 9 laps in 30 minutes, and 1.5 laps in 5 minutes. Adding two columns together also works: 3 + 6 laps take 10 + 20 minutes.

What is a ratio table for division?

A ratio table can scale down as well as up, which is really dividing both values by the same number. With 24 cookies for 8 children, divide both by 2 to get 12 for 4, then by 4 to get 3 for 1. Scaling down to 1 gives the unit rate, 3 cookies per child, which makes any other row easy to fill in.

Is a ratio table a diagram?

A ratio table is usually called a table or chart rather than a diagram, but it plays the same role as a tape diagram or double number line: it is a visual way to show equivalent ratios. Many students like tables because the scale factor between columns is easy to see, and the pairs can be plotted as points on a graph.

Related Topics

• Write a Ratio
• Finding Equivalent Ratio
• Word Problems Involving Writing a Ratio
• Using a Fraction to Write Down a Ratio
• Word Problems Involving Comparing Ratio