Lesson 3: Ratio and Proportion

📥 Introduction

Have you ever tried to follow a recipe that said, “Use 2 cups of flour for every 1 cup of sugar”? That’s a ratio at work! Ratios and proportions help us compare quantities, make fair shares, and scale things up or down.

In this lesson, you’ll learn what ratios and proportions are, how to simplify and solve them, and how they are used in real life — from maps to cooking to sharing money!

🧠 Key Concepts and Explanations

1. What is a Ratio?

A ratio compares two or more quantities. It shows how much of one thing there is compared to another.

Example: If there are 3 boys and 2 girls in a class, the ratio of boys to girls is written as 3:2.

2. Simplifying Ratios

Ratios can be simplified just like fractions — divide both terms by their greatest common factor (GCF).

Example: Simplify 12:16.

• GCF of 12 and 16 is 4.
• 12 ÷ 4 = 3, and 16 ÷ 4 = 4.
• So, 12:16 simplifies to 3:4.

3. What is a Proportion?

A proportion is an equation that says two ratios are equal.

Example: If 2:3 = 4:6, the two ratios form a proportion because they are equivalent.

4. Solving Proportions

To solve a proportion, use cross-multiplication:

If , then .

Example: Solve for x:

• Cross-multiply: 2 × 15 = 5 × x
• 30 = 5x
• Divide both sides by 5: x = 6

5. Real-Life Uses of Ratios and Proportions

• Maps: A map scale might say 1 cm = 5 km (ratio of distance).
• Recipes: Doubling or halving ingredients uses proportions.
• Sharing Money: Dividing profits among partners based on their investment ratios.

📝 Step-by-Step Sample Walkthroughs

Example 1: Simplify the ratio 18:24

• GCF of 18 and 24 is 6.
• 18 ÷ 6 = 3, 24 ÷ 6 = 4.
• Simplified ratio = 3:4.

Example 2: Solve the proportion

• Cross-multiply: 5 × 16 = 8 × x
• 80 = 8x
• Divide both sides by 8: x = 10

Example 3: Word Problem

A drink is mixed in the ratio 2 parts syrup to 5 parts water. If you have 10 parts water, how much syrup should you use?

• Set up proportion:
• Cross-multiply: 2 × 10 = 5 × x
• 20 = 5x
• Divide: x = 4
• You need 4 parts syrup.

✅ Practice Exercises

A. Simplify the Ratios

• 16:24
• 45:60
• 18:27

B. Solve the Proportions

C. True or False?

• 12:18 simplifies to 2:3.
• 

D. Word Problems

1. A map says 1 cm = 8 km. How many kilometers are represented by 3.5 cm?
2. In a school, the ratio of boys to girls is 5:4. If there are 120 boys, how many girls are there?

🔁 Recap

• Ratios compare two or more quantities.
• Simplify ratios by dividing by GCF.
• Proportions show that two ratios are equal — solved by cross-multiplication.
• Ratios and proportions are everywhere: recipes, maps, money sharing!

🪞Reflection Prompt

Think about a time when you shared something with friends (like pizza or airtime). How could you write the sharing as a ratio? Was it fair?