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Equivalent
Ratio Tables

Learn to build, extend, and use ratio tables to find missing values, compare ratios, and solve real-world problems.

6th Grade Math

What Is a Ratio?

A ratio compares two quantities using division. If a recipe calls for 2 cups of flour and 3 cups of sugar, the ratio of flour to sugar is \( 2 : 3 \).

Colon Form
\( 2 : 3 \)
Fraction Form
\( \dfrac{2}{3} \)
Word Form
"2 to 3"

What Are Equivalent Ratios?

Two ratios are equivalent if you can multiply (or divide) both quantities by the same number to get from one ratio to the other.

\( 2 : 3 \)
\( \times 2 \)
\( 4 : 6 \)
\( \times 3 \)
\( 6 : 9 \)
 All three ratios are equivalent
They all simplify to \( 2 : 3 \)

Why Ratio Tables Matter

A ratio table organizes equivalent ratios into rows (or columns) so you can quickly find patterns, fill in missing values, and compare different ratios.

Organize
See all equivalent ratios neatly lined up in one place.
Predict
Extend the pattern to find values you haven't calculated yet.
Compare
Line up two ratio tables to see which rate is better.

The Golden Rule of Ratio Tables

Cups of Flour Cups of Sugar
\( 2 \)
\( 3 \)
\( 4 \)
\( 6 \)
\( 6 \)
\( 9 \)
\( 10 \)
\( 15 \)
\( \times 2 \)
\( \times 3 \)
\( \times 5 \)
 Each row = original ratio × same multiplier

Building a Ratio Table

Two strategies to fill in a ratio table:

Multiply Up
Start with the simplest ratio and multiply both columns by \( 2, 3, 4, \ldots \) to generate new rows.
Add the Ratio
Add the original amounts to each column repeatedly: \( +2 \) to flour, \( +3 \) to sugar each row.

Additive vs. Multiplicative Thinking

Additive Pattern Multiplicative Pattern
Method Add the same amounts to each column Multiply both columns by the same factor
Example \( 2, 4, 6, 8 \ldots \) (add \( +2 \)) \( 2 \times 1, 2 \times 2, 2 \times 3 \ldots \)
Best for Next consecutive row Jumping to any row (e.g., the 10th)
Caution Only add to both columns Only multiply both columns

How to Solve with Ratio Tables

1
Write the known ratio as the first row of your table.
2
Identify the target: which value is missing and which column does it belong to?
3
Find the multiplier: divide the known target value by the matching value in row 1.
4
Apply the multiplier to the other column to find the missing value.
5
Check: Does your new ratio simplify back to the original? If yes, you're done.

Example 1: Lemonade Recipe

A recipe uses 4 lemons for every 6 cups of water. How many cups of water do you need for 10 lemons?

Lemons Cups of Water
\( 4 \)
\( 6 \)
\( 8 \)
\( 12 \)
\( 10 \)
?
\( \times 2.5 \)
Multiplier: \( 10 \div 4 = 2.5 \)
\( 6 \times 2.5 = 15 \) cups of water

Example 2: Finding a Missing Value

A car travels 3 miles every 5 minutes. Complete the table below:

Miles Minutes
\( 3 \)
\( 5 \)
\( 6 \)
\( 10 \)
\( 9 \)
\( 15 \)
?
\( 25 \)
\( \times 5 \)
\( 25 \div 5 = 5 \), so multiply by \( 5 \)
\( 3 \times 5 = 15 \) miles

Plotting on the Coordinate Plane

Each row of a ratio table gives an ordered pair \( (x, y) \). Plot them and they form a straight line through the origin.

0 1 2 3 4 1 2 3 4 5 6 Lemons (x) Cups of Water (y)
\( (2, 3) \)
\( (4, 6) \)
 Straight line!

Comparing Ratios with Tables

Store A sells 3 apples for $2. Store B sells 5 apples for $4. Which is the better deal?

Store A: 3 apples for $2 Apples Cost ($)
\( 3 \)
\( 2 \)
\( 6 \)
\( 4 \)
\( 9 \)
\( 6 \)
\( 15 \)
\( 10 \)
 Store B: 5 apples for $4 Apples Cost ($)
\( 5 \)
\( 4 \)
\( 10 \)
\( 8 \)
\( 15 \)
\( 12 \)
At 15 apples:
Store A = $10 vs Store B = $12 → Store A wins!

Example 3: Scaling Up

A factory makes 7 toys every 2 hours. How many toys are made in 14 hours?

1
Base ratio: \( 7 \) toys per \( 2 \) hours.
2
Find multiplier: \( 14 \div 2 = 7 \).
3
Apply to both: \( 7 \times 7 = 49 \) toys and \( 2 \times 7 = 14 \) hours.

Common Mistakes to Avoid

✕ Only Multiplying One Column
You must multiply both quantities by the same number, not just one.
✕ Adding Instead of Multiplying
Adding a fixed number to each column doesn't preserve the ratio. \( 2 : 3 \) + 1 each = \( 3 : 4 \), which is not equivalent.
✕ Swapping the Order
The ratio \( 3 : 5 \) is not the same as \( 5 : 3 \). Keep the quantities in the correct columns.

Summary: Key Concepts

Concept What It Means Example
Ratio Comparison of two quantities \( 2 : 5 \)
Equivalent Ratio Same ratio, different scale \( 4 : 10 \)
Ratio Table Organized list of equivalent ratios Rows: \( 2, 4, 6 \ldots \)
Multiplier Scale factor between rows \( \times 3 \) to both columns
Coordinate Plot Pairs form a straight line Through \( (0, 0) \)

Question 1 of 5

The ratio of red beads to blue beads is \( 4 : 7 \). If there are 28 blue beads, how many red beads are there?

Question 2 of 5

Which ratio is equivalent to \( 6 : 9 \)?

Question 3 of 5

A table shows the ratio \( 5 : 8 \). The next rows are \( 10 : 16 \), \( 15 : 24 \), and \( 20 : \text{?} \). What is the missing value?

Question 4 of 5

Store X sells 4 notebooks for $6. Store Y sells 6 notebooks for $10. Which store offers the better price per notebook?

Question 5 of 5

When you plot equivalent ratio pairs on a coordinate plane, the points always form: