What Are Equivalent Ratios?
Equivalent ratios are different ratios that express the same relationship between numbers.
Just like equivalent fractions (½ and 2/4 are the same), equivalent ratios show the same comparison between quantities, even if the numbers look different. They're super useful in recipes, maps, and when comparing things in everyday life!
How to Find Equivalent Ratios
1️⃣ Multiply or divide both numbers in the ratio by the same number
2️⃣ Simplify the ratio to its smallest form (like simplifying fractions)
3️⃣ Check if the simplified forms are identical
Let's Explore with Examples!
Example 1: Colorful Blocks
In a box, there are 2 blue blocks for every 3 green blocks (ratio 2:3). If we double the number of blocks, what's the equivalent ratio?
When we double both numbers: 2 × 2 = 4 blue blocks and 3 × 2 = 6 green blocks.
The equivalent ratio is 4:6! Both 2:3 and 4:6 represent the same relationship.
Example 2: Lemonade Recipe
A lemonade recipe uses 3 lemons for every 2 cups of water (3:2). If you want to make a bigger batch using 9 lemons, how much water should you use to keep the same flavor?
Think: How many times bigger is 9 lemons compared to 3 lemons?
Multiply both numbers in the ratio by that same number!
Solution: 3 × 3 = 9 lemons, so 2 × 3 = 6 cups of water.
The equivalent ratio is 9:6 - same great lemonade taste!
Parent Tips 🌟
- Cooking conversions are perfect for practicing equivalent ratios - double a recipe together and calculate the new amounts!
- Use building blocks or LEGO to create visual ratio models that kids can rearrange to find equivalents.
- Point out real-world examples like sports statistics ("This player makes 2 baskets every 5 shots - that's the same as 4 baskets every 10 shots").