Advanced Ratios & Proportions

Apply proportions to percentages, taxes, discounts, unit conversions, and real-world scenarios.

7th Grade

Proportions

~45 min

🎮 Interactive Activity: Proportion Solver

Solve proportions using cross multiplication!

3 / 4 = 12 / x

🎮 Interactive Activity: Percentage Calculator

Calculate percentages from parts and wholes!

25 out of 100 = ?%

1. Understanding Ratios

What is a Ratio?

A ratio compares two quantities. It can be written as a:b, a/b, or "a to b".

Example 1: Simplifying Ratios

Simplify the ratio 18:24

Step 1: Find the GCF of 18 and 24: GCF = 6

Step 2: Divide both by 6: 18÷6 : 24÷6 = 3:4

Answer: 3:4

Example 2: Equivalent Ratios

Find ratios equivalent to 2:3

2:3 = 4:6 = 6:9 = 8:12 = 10:15

Method: multiply both numbers by the same number simultaneously

Key Concepts:

• Ratio comparison: Comparison relationship between two quantities of the same kind
• Simplification: Always simplify ratios to their simplest form (find the greatest common divisor)
• Order is important: 3:4 and 4:3 are different ratios
• Real-world applications: Recipes, map scales, mixing ratios, etc.

2. Solving Proportions

3. Percentages & Applications

4. Unit Rates & Conversions

5. Problem-Solving Strategies

6. Real-World Applications

Frequently Asked Questions

Practice Time!

Practice Quiz

Questions

Correct

Score

If 3/5 = x/25, what is x?

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A shirt costs $40. With a 20% discount, what is the sale price?

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If 5 miles = 8 kilometers, how many kilometers is 15 miles?

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What is 15% of 80?

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A recipe calls for 2 cups flour for 4 servings. How much flour for 10 servings?

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If a car travels 240 miles in 4 hours, what is the unit rate?

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A map scale is 1:25000. If two cities are 3 cm apart on the map, how far are they in real life?

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What percentage is 18 out of 60?

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If 8 workers can build a wall in 6 days, how many days for 12 workers?

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A store marks up items by 30%. If cost is $50, what is the selling price?

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