Equivalent Ratio Tables
What Are They? 🤔
Equivalent ratios are different pairs of numbers that represent the same relationship. A ratio table is a tool that organizes these equivalent ratios. They are useful for scaling recipes, comparing prices, and solving real-world problems!
How to Build a Ratio Table
- Start with your original ratio.
- Multiply or Divide both parts of the ratio by the same number.
- Fill in the table with your new equivalent ratios.
Examples in Action
Example 1: The Lemonade Recipe
For 2 cups of juice, you need 3 cups of water. Complete the table for 4 and 6 cups of juice.
Step 1: Start ratio: 2 juice : 3 water
Step 2: To get 4 juice, multiply by 2. So, 3 water × 2 = 6 water.
Step 3: To get 6 juice, multiply the original by 3. So, 3 water × 3 = 9 water.
| Juice (cups) | 2 | 4 | 6 |
|---|---|---|---|
| Water (cups) | 3 | 6 | 9 |
Example 2: Dog Walking
You earn $15 for walking 3 dogs. How much for 6 dogs? 1 dog?
Step 1: Ratio: 15 dollars : 3 dogs
Step 2: Find the unit rate. Divide both by 3: 5 dollars : 1 dog.
Step 3: For 6 dogs, multiply the unit rate by 6: 5 × 6 = 30 dollars.
| Dollars | 15 | 5 | 30 |
|---|---|---|---|
| Dogs | 3 | 1 | 6 |
Common Mistakes to Avoid 🚫
- Forgetting the Rule: You MUST multiply or divide both sides by the same number. Changing one side differently breaks the relationship.
- Adding/Subtracting: Don't just add the same number to both sides. This doesn't create an equivalent ratio. (2:3 is NOT equivalent to 4:5).
Tips & Tricks 💡
- Find the Unit Rate: Dividing to find the value for "1" (like dollars per dog) makes it easy to find any other value.
- Check Your Work: Cross-multiply to check if two ratios are equivalent. If 2/3 = 4/6, then 2×6 should equal 3×4. (12 = 12 ✔️)
How to Practice
1. Use Real Life: Double a recipe. Calculate the cost of multiple items.
2. Fill in the Blanks: Create tables with missing values and solve for them.
3. Play Games: Online math games often have ratio activities!