Skip to content

Introduction to Ratios

Learn what ratios are and how to write them in different forms

Written and reviewed by the Study Mondo Education TeamLast updated
🎯⭐ INTERACTIVE LESSON

Try the Interactive Version!

Learn step-by-step with practice exercises built right in.

Start Interactive Lesson →

Introduction to Ratios

What is a Ratio?

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

Ways to Write Ratios

If there are 3 apples and 5 oranges, the ratio of apples to oranges can be written three ways:

  1. Using "to": 3 to 5
  2. Using a colon: 3:5
  3. As a fraction: 35\frac{3}{5}

Simplifying Ratios

Like fractions, ratios should be written in simplest form.

Example: The ratio 6:8 simplifies to 3:4 (divide both by 2)

Part-to-Part vs Part-to-Whole

  • Part-to-Part: Compares one part to another part

    • Example: 3 boys to 5 girls → 3:5

  • Part-to-Whole: Compares one part to the total

    • Example: 3 boys out of 8 total students → 3:8

Equivalent Ratios

Ratios are equivalent if they represent the same comparison: 2:3=4:6=6:9=8:122:3 = 4:6 = 6:9 = 8:12

(Multiply or divide both parts by the same number)

📚 Practice Problems

1Problem 1easy

❓ Question:

Write the ratio of stars to hearts in simplest form: ⭐⭐⭐⭐⭐⭐ ❤️❤️❤️

💡 Show Solution

Solution:

Count: 6 stars and 3 hearts

Ratio: 6:36:3

Simplify by dividing both by 3: 6:3=2:16:3 = 2:1

Answer: The ratio is 2:12:1 (or 2 to 1)

2Problem 2medium

❓ Question:

A recipe calls for 2 cups of flour and 3 cups of sugar. If you want to make the recipe using 8 cups of flour, how much sugar do you need?

💡 Show Solution

Solution:

Original ratio: 2:32:3 (flour to sugar)

Flour increased from 2 to 8 (multiplied by 4): 2×4=82 \times 4 = 8

Sugar must also multiply by 4: 3×4=123 \times 4 = 12

Answer: You need 12 cups of sugar

3Problem 3hard

❓ Question:

In a class of 24 students, the ratio of girls to boys is 5:3. How many girls and how many boys are in the class?

💡 Show Solution

Solution:

Ratio parts: 5+3=85 + 3 = 8 total parts

Each part represents: 24÷8=3 students24 \div 8 = 3 \text{ students}

Girls: 5×3=155 \times 3 = 15 students Boys: 3×3=93 \times 3 = 9 students

Check: 15+9=2415 + 9 = 24 ✓

Answer: 15 girls and 9 boys

Explain using:
Next Topic →
Unit Rates
🎴

Practice with Flashcards

Rate this topic's cards with spaced repetition. Cards join your deck when you finish a topic's lesson and take its exit quiz.

📖

Browse All Topics

Explore more Grade 6 Math topics

📌 Related Topics in Ratios and Rates

Unit Rates

❓ Frequently Asked Questions

What is Introduction to Ratios?▾
Learn what ratios are and how to write them in different forms
How can I study Introduction to Ratios effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 3 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Introduction to Ratios study guide free?▾
Yes — all study notes, flashcards, and practice problems for Introduction to Ratios on Study Mondo are free to access. No account is needed.
What course covers Introduction to Ratios?▾
Introduction to Ratios is part of the Grade 6 Math course on Study Mondo, specifically in the Ratios and Rates section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Introduction to Ratios?▾
Yes, this page includes 3 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.