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