Simplify Ratio Calculator

Ratio Simplifier Calculator

function gcd(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var temp = b; b = a % b; a = temp; } return a; } function calculateSimplifiedRatio() { var firstNumberInput = document.getElementById("firstNumber").value; var secondNumberInput = document.getElementById("secondNumber").value; var resultDiv = document.getElementById("result"); var num1 = parseInt(firstNumberInput); var num2 = parseInt(secondNumberInput); if (isNaN(num1) || isNaN(num2) || num1 <= 0 || num2 <= 0) { resultDiv.innerHTML = "Please enter valid positive whole numbers for both fields."; return; } var commonDivisor = gcd(num1, num2); var simplifiedNum1 = num1 / commonDivisor; var simplifiedNum2 = num2 / commonDivisor; resultDiv.innerHTML = "The simplified ratio is: " + simplifiedNum1 + " : " + simplifiedNum2 + ""; }

Understanding and Simplifying Ratios

A ratio is a mathematical expression that compares two or more quantities of the same kind. It shows how much of one quantity there is compared to another. Ratios are commonly used in everyday life, from cooking recipes to map scales, and in various scientific and engineering fields.

What is a Ratio?

A ratio can be written in several ways: using a colon (e.g., 3:4), using the word "to" (e.g., 3 to 4), or as a fraction (e.g., 3/4). Regardless of the notation, it represents the relationship between the quantities. For instance, if a recipe calls for 2 cups of flour to 1 cup of sugar, the ratio of flour to sugar is 2:1.

Why Simplify Ratios?

Simplifying a ratio means reducing it to its lowest whole number terms, much like simplifying a fraction. This makes the ratio easier to understand and compare. For example, a ratio of 10:15 is mathematically equivalent to 2:3, but 2:3 is simpler and more intuitive to grasp. Simplified ratios help in:

• Clarity: Easier to interpret the relationship between quantities.
• Comparison: Allows for quick comparison with other ratios.
• Standardization: Provides a standard form for ratios.

How to Simplify a Ratio

To simplify a ratio, you need to find the Greatest Common Divisor (GCD) of the numbers in the ratio. The GCD is the largest positive integer that divides both numbers without leaving a remainder. Once you find the GCD, you divide each number in the ratio by this GCD.

Here's the step-by-step process:

1. Identify the numbers: Take the two numbers that form your ratio (e.g., A:B).
2. Find the GCD: Determine the Greatest Common Divisor of A and B.
3. Divide by the GCD: Divide both A and B by their GCD.
4. Write the simplified ratio: The resulting numbers form your simplified ratio.

Examples of Ratio Simplification

• Example 1: Simplify 10:15
  • Numbers are 10 and 15.
  • The common divisors of 10 are 1, 2, 5, 10.
  • The common divisors of 15 are 1, 3, 5, 15.
  • The Greatest Common Divisor (GCD) of 10 and 15 is 5.
  • Divide both numbers by 5: 10 ÷ 5 = 2 and 15 ÷ 5 = 3.
  • The simplified ratio is 2:3.
• Example 2: Simplify 24:36
  • Numbers are 24 and 36.
  • The GCD of 24 and 36 is 12.
  • Divide both numbers by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3.
  • The simplified ratio is 2:3.
• Example 3: Simplify 7:21
  • Numbers are 7 and 21.
  • The GCD of 7 and 21 is 7.
  • Divide both numbers by 7: 7 ÷ 7 = 1 and 21 ÷ 7 = 3.
  • The simplified ratio is 1:3.

Use the calculator above to quickly simplify any two-part ratio to its lowest whole number terms!