Fraction Calculator with Whole Numbers

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Fraction Calculator with Whole Numbers

Easily add, subtract, multiply, and divide mixed numbers

+ − × ÷

Result:

Understanding Mixed Number Fractions

A fraction with a whole number, also known as a mixed number, consists of an integer and a proper fraction. Dealing with these in mathematics is a common task in woodworking, cooking, and engineering where measurements are rarely simple integers.

How to Calculate Fractions with Whole Numbers

To manually calculate operations on mixed numbers, follow these standard steps:

  1. Convert to Improper Fractions: Multiply the whole number by the denominator and add the numerator. Keep the original denominator.
    Example: 2 1/4 = (2 × 4 + 1) / 4 = 9/4
  2. Perform the Operation:
    • Addition/Subtraction: Find a common denominator, adjust the numerators, and perform the math.
    • Multiplication: Multiply numerators together and denominators together.
    • Division: Flip the second fraction (reciprocal) and multiply.
  3. Simplify: Reduce the resulting fraction to its lowest terms by finding the Greatest Common Divisor (GCD).
  4. Convert Back: If the numerator is larger than the denominator, convert it back into a mixed number.

Practical Example: Woodworking

Imagine you have a piece of wood that is 5 3/4 inches long and you need to cut off 2 7/8 inches.

  • Convert 5 3/4 to 23/4 (which is 46/8).
  • Convert 2 7/8 to 23/8.
  • Subtract: 46/8 – 23/8 = 23/8.
  • Result: 2 7/8 inches remaining.
function calculateFraction() { var w1 = parseInt(document.getElementById('whole1').value) || 0; var n1 = parseInt(document.getElementById('num1').value) || 0; var d1 = parseInt(document.getElementById('den1').value) || 1; var w2 = parseInt(document.getElementById('whole2').value) || 0; var n2 = parseInt(document.getElementById('num2').value) || 0; var d2 = parseInt(document.getElementById('den2').value) || 1; var op = document.getElementById('operator').value; if (d1 === 0 || d2 === 0) { alert("Denominator cannot be zero."); return; } // Convert to improper fractions // (Whole * Denom + Num) / Denom var improperNum1 = (Math.abs(w1) * d1) + n1; if (w1 < 0) improperNum1 *= -1; var improperNum2 = (Math.abs(w2) * d2) + n2; if (w2 < 0) improperNum2 *= -1; var resNum, resDen; if (op === 'add') { resNum = (improperNum1 * d2) + (improperNum2 * d1); resDen = d1 * d2; } else if (op === 'subtract') { resNum = (improperNum1 * d2) – (improperNum2 * d1); resDen = d1 * d2; } else if (op === 'multiply') { resNum = improperNum1 * improperNum2; resDen = d1 * d2; } else if (op === 'divide') { if (improperNum2 === 0) { alert("Cannot divide by zero."); return; } resNum = improperNum1 * d2; resDen = d1 * improperNum2; } // Handle sign if (resDen = resDen) { finalWhole = (resNum > 0) ? Math.floor(resNum / resDen) : Math.ceil(resNum / resDen); finalNum = Math.abs(resNum % resDen); } var resultBox = document.getElementById('result-box'); var resultDisplay = document.getElementById('result-display'); var decimalResult = document.getElementById('decimal-result'); var html = ""; if (finalWhole !== 0) { html += finalWhole + " "; } if (finalNum !== 0) { html += '
' + '' + finalNum + '' + '' + finalDen + '' + '
'; } if (finalWhole === 0 && finalNum === 0) { html = "0"; } resultDisplay.innerHTML = html; decimalResult.innerHTML = "Decimal Equivalent: " + (resNum / resDen).toFixed(4); resultBox.style.display = "block"; } function gcd(a, b) { return b ? gcd(b, a % b) : a; }

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