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.

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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.

145

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

How is a ratio table different from a proportion?

A proportion is an equation stating that two ratios are equal (e.g., \(\color{blue}{\frac{2}{3} = \frac{4}{6}}\)). A ratio table is a collection of multiple equivalent ratios organized in rows — essentially a set of proportions all related to the same original ratio.

Can a ratio table have more than two columns?

Yes — if three or more quantities are in a fixed ratio, the table can have three or more columns, each column tracking one quantity. The key is that every row still represents the same fixed relationship.

When is a ratio table more useful than cross-multiplication?

Ratio tables are especially helpful when you need to find several equivalent values, not just one. For a single unknown, cross-multiplication is faster; for filling in a full table or spotting patterns, the table approach is more efficient.

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