🔢 Ratio Ranger 🏹
Your ultimate companion for mastering ratios in middle school math! Learn, practice, and visualize ratios with our interactive tools.
📊 What Are Ratios?
A ratio compares two or more quantities, showing the relative sizes of each. Ratios are everywhere in real life – from mixing ingredients in recipes to comparing speeds of cars.
Ratios can be written in three ways:
Ratios can be simplified just like fractions by dividing both numbers by their greatest common factor.
🍪 Baking Cookies
A recipe uses a 2:3 ratio of sugar to flour. For every 2 cups of sugar, you need 3 cups of flour.
🚗 Speed Comparison
Car A travels 60 mph while Car B travels 45 mph. The ratio of their speeds is 60:45, which simplifies to 4:3.
🏀 Basketball Team
A team has 12 players with a 5:7 ratio of boys to girls. This means for every 5 boys, there are 7 girls.
Ratios are used in many areas of math and daily life:
- 📐 Geometry: Similar figures have proportional side lengths
- 📈 Percentages: A percentage is a ratio out of 100
- ⚖️ Scaling: Enlarging or reducing sizes while maintaining proportions
- 🧪 Science: Chemical formulas show ratios of elements
🧮 Ratio Calculator
Enter two numbers to calculate their ratio in different forms.
Ratio Results
Enter numbers and click “Calculate Ratio” to see results.
✨ Ratio Simplifier
Enter a ratio to simplify it to its lowest terms.
Simplified Ratio
Enter numbers and click “Simplify Ratio” to see results.
🔢 Ratio Converter
Convert between ratio, fraction, decimal, and percentage forms.
Converted Forms
Enter numbers and click “Convert Ratio” to see different forms.
📝 Practice Problems
Test your ratio skills with these practice problems. Try to solve them yourself before checking the solutions!
Problem 1: Simplifying Ratios
Simplify the ratio 18:24 to its lowest terms.
Solution:
To simplify 18:24:
- Find the greatest common factor (GCF) of 18 and 24. The factors of 18 are 1, 2, 3, 6, 9, 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The GCF is 6.
- Divide both numbers by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
- The simplified ratio is 3:4.
Problem 2: Equivalent Ratios
Find two equivalent ratios for 5:7.
Solution:
To find equivalent ratios, multiply or divide both numbers by the same value:
- Multiply by 2: (5×2):(7×2) = 10:14
- Multiply by 3: (5×3):(7×3) = 15:21
So two equivalent ratios are 10:14 and 15:21.
Problem 3: Real-World Application
A fruit punch recipe calls for orange juice and pineapple juice in a 3:5 ratio. If you use 9 cups of orange juice, how many cups of pineapple juice should you use?
Solution:
This is a proportion problem where we set up equivalent ratios:
- The original ratio is 3:5 (orange:pineapple).
- We have 9 cups of orange juice, which is 3 × 3.
- To maintain the ratio, multiply the pineapple amount by the same factor: 5 × 3 = 15.
- Therefore, you should use 15 cups of pineapple juice.
We can check this by seeing that 3:5 = 9:15 (both ratios simplify to 3:5).
📈 Ratio Visualization
Understanding ratios becomes easier when you can visualize them. Try entering different numbers below to see how the ratio changes visually.