📊 Ratio Basics

A ratio shows how two quantities compare. It can be written using "to," a colon, or as a fraction.

🎯 What You'll Learn

Understand what ratios mean and represent
Write ratios in different ways
Simplify ratios to their simplest form
Apply ratios to real-world scenarios

✏️ Explanation

A ratio shows how two quantities compare. It can be written using "to," a colon, or as a fraction.

🔍 Why It Matters

Ratios are used in recipes, maps, and sharing quantities fairly. They help us understand proportions in cooking, scaling drawings, and dividing resources.

🧭 Understanding Ratios

Using "to"

10 to 15

Read as "10 to 15"

Using colon (:)

10:15

Most common way to write ratios

As a fraction

10/15

Useful for simplifying

Simplified

2:3

Divide both by their GCD (5)

✏️ Worked Example

In a class of 10 boys and 15 girls, what is the ratio of boys to girls?

Step 1: Identify the quantities

Boys = 10, Girls = 15

Step 2: Write the ratio (order matters!)

Boys to Girls = 10:15

Step 3: Simplify by finding the GCD

GCD of 10 and 15 = 5

Step 4: Divide both numbers by the GCD

10 ÷ 5 = 2, 15 ÷ 5 = 3

Answer: The ratio of boys to girls is 10:15 or 2:3 in simplified form

🌍 Ratio Examples

🍪 Recipe Ratios

A cookie recipe uses 2 cups of flour for every 1 cup of sugar

Flour to Sugar = 2:1

🎨 Paint Mixing

To make purple paint, mix 3 parts blue with 2 parts red

Blue to Red = 3:2

🗺️ Map Scale

On a map, 1 cm represents 5 km in real life

Map to Reality = 1:500,000

⚽ Sports Teams

A football team has 11 players on field, 7 substitutes

Players to Subs = 11:7

🧮 Ratio Calculator & Simplifier

Ratio in Different Forms:

Using "to"

10 to 15

Using colon

10:15

As fraction

10/15

Simplified

2:3

Step 1: Find the GCD (Greatest Common Divisor)

GCD of 10 and 15 = 5

Step 2: Divide both numbers by the GCD

10 ÷ 5 = 2, 15 ÷ 5 = 3

Step 3: Simplified ratio

10:15 = 2:3

🔢 Practice Exercises

1. Write the ratio of 6 cats to 9 dogs

2. Simplify the ratio 12:16

3. If a recipe uses 2 cups of sugar for 3 cups of flour, what is the ratio of sugar to flour?

4. What's the ratio of 5 red marbles to 20 total marbles?

5. Express 8:12 in its simplest form

⚠️ Common Mistakes

Writing the quantities in the wrong order
Not simplifying the ratio
Confusing ratios with fractions

✨ Quick Summary

Ratios compare values and can be simplified just like fractions.