Ratio Calculator

Solve and Simplify Ratios

This versatile Ratio Calculator has two key functions: simplifying a ratio to its lowest integer terms, and solving for a missing value in a proportion.

The Formulas Explained

• Simplify Ratio: To simplify a ratio a:b, the calculator finds the Greatest Common Factor (GCF) of a and b and then divides both numbers by it.
• Solve for X: To solve a proportion a : b = c : x, the calculator uses the cross-multiplication principle: a * x = b * c. It then solves for x with the formula x = (b * c) / a.

How to Use the Calculator

• To Simplify: Select the 'Simplify Ratio' tab, enter the two parts of your ratio, and click 'Calculate'.
• To Solve for X: Select the 'Solve for X' tab, enter the three known values of the proportion, and click 'Calculate'.

Real-World Examples

• Simplifying a Ratio: You have a classroom with 18 boys and 24 girls. You want to find the simplified ratio of boys to girls.
  • Enter 18 and 24. The GCF is 6.
  • The simplified ratio is 18/6 : 24/6, which is 3 : 4.
• Solving a Proportion: A map has a scale where 2 inches represents 5 miles. You measure a distance of 7 inches on the map. How many miles is that in reality?
  • Set up the proportion 2 : 5 = 7 : x.
  • Enter a=2, b=5, and c=7.
  • Calculation: x = (5 * 7) / 2 = 17.5. The distance is 17.5 miles.

Frequently Asked Questions (FAQ)

• Can I simplify a ratio with more than two numbers? This calculator is designed for two-part ratios. To simplify a ratio like a:b:c, you would find the GCF of all three numbers and divide each by it.
• What is a ratio? A ratio shows the relative sizes of two or more values. It tells you how much of one thing there is compared to another thing.
• What is a proportion? A proportion is an equation stating that two ratios are equal.