Rational Calculator

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Rational Number Calculator

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What is a Rational Calculator?

A rational calculator is a specialized mathematical tool designed to perform operations on rational numbers—values that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Unlike standard calculators that convert everything to decimals immediately, this tool maintains the integrity of the ratio, providing simplified fractional outputs.

Understanding Rational Numbers

Rational numbers include all integers, fractions, and repeating or terminating decimals. In technical fields like engineering, music theory, and woodworking, keeping numbers in their rational (fractional) form prevents "rounding errors" that accumulate when using decimals prematurely.

How the Calculation Works

To calculate the sum, difference, product, or quotient of two rational numbers, we follow these fundamental algebraic rules:

  • Addition/Subtraction: Requires a common denominator. For a/b ± c/d, the formula is (ad ± bc) / bd.
  • Multiplication: Simply multiply the numerators and the denominators: (a * c) / (b * d).
  • Division: Multiply the first fraction by the reciprocal of the second: (a * d) / (b * c).

Practical Example: Woodworking

Imagine you are building a shelf. You have a board that is 3/4 of a meter long, and you need to cut a piece that is 1/3 of a meter long. To find the remaining length, you subtract 1/3 from 3/4:

  1. Find a common denominator (12).
  2. Convert: 9/12 – 4/12.
  3. Result: 5/12 of a meter.

Using the rational calculator above, you can skip the manual conversion and get the simplified result instantly.

Simplifying the Result

Our calculator automatically simplifies the result to its lowest terms by finding the Greatest Common Divisor (GCD). For instance, if the raw calculation yields 10/20, the tool will automatically reduce it to 1/2 for easier interpretation.

function performRationalCalculation() { var n1 = parseInt(document.getElementById('num1').value); var d1 = parseInt(document.getElementById('den1').value); var n2 = parseInt(document.getElementById('num2').value); var d2 = parseInt(document.getElementById('den2').value); var op = document.getElementById('operator').value; var resultDiv = document.getElementById('rationalResult'); var fracDisp = document.getElementById('fractionalDisplay'); var decDisp = document.getElementById('decimalDisplay'); if (isNaN(n1) || isNaN(d1) || isNaN(n2) || isNaN(d2)) { alert("Please enter valid integers in all fields."); return; } if (d1 === 0 || d2 === 0) { alert("Denominator cannot be zero."); return; } var resNum, resDen; if (op === 'add') { resNum = (n1 * d2) + (n2 * d1); resDen = d1 * d2; } else if (op === 'subtract') { resNum = (n1 * d2) – (n2 * d1); resDen = d1 * d2; } else if (op === 'multiply') { resNum = n1 * n2; resDen = d1 * d2; } else if (op === 'divide') { if (n2 === 0) { alert("Cannot divide by zero."); return; } resNum = n1 * d2; resDen = d1 * n2; } // Simplification logic (Greatest Common Divisor) var findGCD = function(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var t = b; b = a % b; a = t; } return a; }; var common = findGCD(resNum, resDen); var simplifiedNum = resNum / common; var simplifiedDen = resDen / common; // Handle signs if (simplifiedDen < 0) { simplifiedNum = -simplifiedNum; simplifiedDen = -simplifiedDen; } resultDiv.style.display = 'block'; if (simplifiedDen === 1) { fracDisp.innerText = simplifiedNum; } else { fracDisp.innerText = simplifiedNum + " / " + simplifiedDen; } var decimalVal = (resNum / resDen).toFixed(4); decDisp.innerText = "Decimal Equivalent: " + decimalVal.replace(/\.?0+$/, ""); }

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