Identify equivalent ratios

key notes :

📖 What is a Ratio?

A ratio compares two or more quantities.

Example: 2:3 means for every 2 of one thing, there are 3 of another.

Can also be written as fractions: 2:3 = 2/3 ✅

⚖️ Equivalent Ratios

Two ratios are equivalent if they express the same relationship.

Example: 2:3 and 4:6 are equivalent because:

2/3 = 4/6

✖️ Multiplying or Dividing to Find Equivalent Ratios

Multiply or divide both terms of a ratio by the same number.

Example: 5:8 → multiply by 2 → 10:16 ✅

Example: 12:18 → divide by 6 → 2:3 ✅

🔄 Cross Multiplication Method

To check if two ratios are equivalent:

For ratios a:b and c:d, check if:

a×d = b×c

Example: Are 3:4 and 9:12 equivalent?

3×12=36 , 4×9=36 ✅

📊 Using Tables to Identify Equivalent Ratios

• Make a table of multiples to see if ratios match:

Ratio 1	Ratio 2
2	4
3	6

✅ Both ratios are equivalent.

🎯 Tip for Quick Recognition

Reduce ratios to lowest terms.

If reduced ratios are the same, they are equivalent.

💡 Real-Life Examples

Cooking 🍲: 2 cups flour : 1 cup sugar → 4:2 is equivalent.

Maps 🗺️: 1 cm : 5 km → 2 cm : 10 km is equivalent.

Mixing colors 🎨: 3 red : 2 blue → 6 red : 4 blue is equivalent.

Learn with an example

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