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Understanding Proportions Notes

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Understanding Proportions Notes

Proportions illustration

📚 Key Definitions and "I Can" Statements

Learning Goals - Read and check off when you understand:

I can identify proportions as pairs of equivalent ratios

I can determine if two ratios form a proportion using cross-multiplication

I can create my own proportions using real-world examples

Key Terms:

Ratio: A comparison of two quantities (Example: 2:4 or 2/4)

Proportion: Two ratios that show the same relationship

Example: 1/2 = 2/4 (This IS a proportion because both ratios are equal)

Write your own definition of proportion in simple words:

🔍 Identifying Proportions - Cross-Multiplication Method

Steps to check if two ratios form a proportion:

Step 1: Write the two ratios as fractions

Step 2: Cross-multiply (multiply diagonally)

Step 3: If the products are equal, it's a proportion!

Example: Does 2/3 = 4/6?

Cross-multiply: 2 × 6 = _____ and 3 × 4 = _____

Since 12 = 12, this _____ a proportion. (Circle: IS or IS NOT)

Try it yourself: Does 3/4 = 6/8?
Which pairs form proportions? Use cross-multiplication to check:

1/2 and 3/6

2/5 and 4/10

3/7 and 6/12

🌟 Real-World Proportions and Reflection

Real-world examples where we use proportions:

• Recipes (2 cups flour for 1 cake = 4 cups flour for 2 cakes)

• Maps (1 inch = 10 miles)

• Shopping (3 apples for $2 = 6 apples for $4)

Create your own real-world proportion example:
Write one pair of ratios that form a proportion and prove it using cross-multiplication:
Complete this sentence: "I can identify and create proportions because..."

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