Grade: Grade 6 Subject: Mathematics Unit: Ratios & Rates SAT: Algebra ACT: Math

Ratio Tables

Learn how to organize equivalent ratios in tables and use them to solve real-world problems.

What is a Ratio Table?

A Ratio Table Shows Equivalent Ratios

A ratio table is an organized way to list pairs of numbers that have the same ratio relationship.

Remember that a ratio compares two quantities. For example, if a recipe uses 2 cups of flour for every 3 cups of sugar, the ratio is 2:3. A ratio table helps us find other amounts that keep the same relationship.

Example: Flour to Sugar Ratio (2:3)

Flour (cups) 2 4 6 8 10
Sugar (cups) 3 6 9 12 15
Multiplier ×1 ×2 ×3 ×4 ×5

Each column shows the same ratio: 2:3 = 4:6 = 6:9 = 8:12 = 10:15

How to Build a Ratio Table

  • Start with the original ratio - Write the first pair of numbers
  • Multiply both numbers by the same value - This keeps the ratio equivalent
  • Continue the pattern - Add as many columns as you need
  • You can also divide! - Use smaller multipliers like 0.5 to go backward

Why Are Ratio Tables Useful?

🍳

Recipes

Scale ingredients up or down while keeping the same taste

🗺️

Maps

Convert between map distances and real distances

💰

Shopping

Compare prices and find the best deals

⚗️

Science

Mix solutions and chemicals in correct proportions

The Golden Rule of Ratio Tables

Remember: Whatever you do to ONE row, you must do to the OTHER row! If you multiply the top by 3, multiply the bottom by 3. If you divide the top by 2, divide the bottom by 2. This keeps the ratio equivalent.

Finding Missing Values

Ratio tables are especially helpful when you need to find a missing value. Look at this example:

Find the Missing Value

Miles 5 10 15 ?
Hours 1 2 3 4

Solution: The pattern shows miles = 5 × hours. So when hours = 4, miles = 5 × 4 = 20 miles

Try It: Ratio Table Builder

Enter any starting ratio and watch the table generate equivalent ratios!

Build Your Own Ratio Table

Value A
Value B
Multiplier

Worked Examples

Let's solve some problems using ratio tables step by step.

Example 1: Scaling a Recipe

A cookie recipe uses 3 eggs for every 2 cups of butter. If you want to use 6 cups of butter, how many eggs do you need?
1
Set up the ratio table with what we know:
Eggs : Butter = 3 : 2
Eggs 3 ?
Butter (cups) 2 6
2
Find the multiplier:
We went from 2 cups to 6 cups of butter.
6 ÷ 2 = 3, so the multiplier is 3.
3
Apply the same multiplier to eggs:
3 eggs × 3 = 9 eggs
Answer: You need 9 eggs for 6 cups of butter.

Example 2: Map Distances

On a map, 2 inches represents 50 miles. If two cities are 7 inches apart on the map, how far apart are they in real life?
1
Set up the ratio table:
Inches : Miles = 2 : 50
2
Find the relationship:
For every 2 inches, there are 50 miles.
Per 1 inch: 50 ÷ 2 = 25 miles
Inches 1 2 3 4 5 6 7
Miles 25 50 75 100 125 150 175
3
Find 7 inches:
7 inches × 25 miles per inch = 175 miles
Answer: The cities are 175 miles apart in real life.

Example 3: Unit Price Comparison

Store A sells 4 apples for $3. Store B sells 6 apples for $4. Which store has the better deal?
1
Create ratio tables for both stores to find equivalent amounts:

Store A (4 apples : $3)

Apples 4 8 12
Cost ($) 3 6 9

Store B (6 apples : $4)

Apples 6 12
Cost ($) 4 8
2
Compare at the same number of apples (12):
Store A: 12 apples cost $9
Store B: 12 apples cost $8
Answer: Store B has the better deal ($8 vs $9 for 12 apples).

Practice Problems

Try these problems on your own. Enter your answer and check if you're correct!

Problem 1: Lemonade Recipe

A lemonade recipe uses 4 lemons for every 2 cups of sugar. How many lemons do you need if you use 6 cups of sugar?

Lemons 4 ?
Sugar (cups) 2 6

Problem 2: Driving Distance

A car travels 180 miles in 3 hours. At this rate, how many miles will it travel in 5 hours?

Problem 3: Paint Mixing

To make orange paint, you mix 5 parts red with 3 parts yellow. How many parts of yellow do you need if you use 15 parts of red?

Problem 4: Typing Speed

Sarah types 120 words in 4 minutes. How many words can she type in 7 minutes at the same rate?

Check Your Understanding: Ratio Table Challenge

Test your ratio table skills with this 6-question challenge!

Ratio Table Challenge

Score: 0 / 6
Question 1 of 6

Challenge Complete!

0/6

Next Steps

Key Takeaways:

  • A ratio table organizes equivalent ratios in rows and columns
  • Multiply or divide BOTH values by the same number to keep ratios equivalent
  • Ratio tables help solve real-world problems with recipes, maps, prices, and more
  • Find missing values by identifying the multiplier between known values
  • Practice creating ratio tables with different starting ratios
  • Look for ratio relationships in everyday situations
  • Move on to learn about unit rates in the next lesson