Simplify Calculator

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Simplify Calculator
Simplify a Fraction (A/B)Simplify a Ratio (A:B)Simplify Percentage to Fraction
Result:
function updateLabels(){var mode=document.getElementById('calc_mode').value;var l1=document.getElementById('label1');var l2=document.getElementById('label2');var r2=document.getElementById('row2′);if(mode==='fraction'){l1.innerHTML='Numerator (A):';l2.innerHTML='Denominator (B):';r2.style.display='table-row';}else if(mode==='ratio'){l1.innerHTML='Value A:';l2.innerHTML='Value B:';r2.style.display='table-row';}else if(mode==='percentage'){l1.innerHTML='Percentage (%):';r2.style.display='none';}}function getGCD(a,b){a=Math.abs(a);b=Math.abs(b);while(b){var t=b;b=a%b;a=t;}return a;}function calculateSimplify(){var mode=document.getElementById('calc_mode').value;var v1=parseFloat(document.getElementById('input1').value);var v2=parseFloat(document.getElementById('input2').value);var ansDiv=document.getElementById('answer');var showSteps=document.getElementById('showSteps').checked;if(isNaN(v1)){alert('Please enter a valid number');return;}if(mode!=='percentage'&&isNaN(v2)){alert('Please enter a valid denominator/second value');return;}if(mode!=='percentage'&&v2===0){alert('Denominator cannot be zero');return;}ansDiv.style.display='block';var resultHtml=";if(mode==='percentage'){v2=100;}var commonDivisor=getGCD(v1,v2);var simplifiedA=v1/commonDivisor;var simplifiedB=v2/commonDivisor;if(mode==='fraction'||mode==='percentage'){resultHtml='
'+simplifiedA+' / '+simplifiedB+'
';if(simplifiedB===1){resultHtml='
'+simplifiedA+'
';}resultHtml+='
Decimal: '+(v1/v2).toFixed(4)+'
';}else if(mode==='ratio'){resultHtml='
'+simplifiedA+' : '+simplifiedB+'
';}if(showSteps){resultHtml+='
Steps: The Greatest Common Divisor (GCD) of '+v1+' and '+v2+' is '+commonDivisor+'. Divide both numbers by '+commonDivisor+' to simplify.
';}ansDiv.innerHTML=resultHtml;}

Using the Simplify Calculator

The simplify calculator is a versatile math tool designed to reduce fractions, ratios, and percentages to their simplest form. Whether you are a student working on homework or a professional needing quick conversions, this tool eliminates manual long division and the search for common factors.

To use this calculator, follow these steps:

Choose Mode
Select "Simplify a Fraction", "Simplify a Ratio", or "Simplify Percentage" from the dropdown menu.
Enter Values
Input your numbers into the fields provided. For fractions, enter the numerator (top) and denominator (bottom). For ratios, enter both parts of the comparison.
Calculate
Click "Simplify" to see the reduced result and the greatest common divisor used in the calculation.

How It Works: The Math Behind Simplification

Simplification relies on finding the Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF). The GCD is the largest positive integer that divides each of the integers without a remainder.

The formula for simplifying a fraction A/B is:

Simplified Form = (A ÷ GCD) / (B ÷ GCD)

  • A: The initial numerator or first part of the ratio.
  • B: The initial denominator or second part of the ratio.
  • GCD: The largest number that can divide both A and B evenly.

Our simplify calculator uses the Euclidean Algorithm to find the GCD rapidly, which is far more efficient than listing every factor for large numbers.

Simplification Examples

Example 1: Simplifying a Fraction

Suppose you have the fraction 48/60 and want to simplify it.

  1. Numerator = 48, Denominator = 60
  2. Find factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  3. Find factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  4. The GCD is 12.
  5. Divide 48 by 12 = 4
  6. Divide 60 by 12 = 5
  7. Result: 4/5

Example 2: Simplifying a Ratio

Simplify the ratio 150:250.

  1. Value A = 150, Value B = 250
  2. The GCD of 150 and 250 is 50.
  3. 150 ÷ 50 = 3
  4. 250 ÷ 50 = 5
  5. Simplified Ratio: 3:5

Common Questions

What is a simplified fraction?

A simplified fraction (or a fraction in lowest terms) is a fraction where the numerator and denominator have no common divisors other than 1. For example, 2/3 is simplified, but 4/6 is not because both numbers can be divided by 2.

Can the simplify calculator handle decimals?

This specific calculator is designed for integers. To simplify a fraction with decimals, you should first multiply both the top and bottom by 10, 100, or 1000 to convert them to whole numbers, then use the simplify calculator.

Why is simplifying fractions important?

Simplifying makes mathematical expressions easier to read, compare, and use in further calculations. It provides a standard "lowest term" that makes it clear how different parts of a whole relate to one another.

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