Mixed Fractions Calculator

Use this calculator to perform addition, subtraction, multiplication, or division on two mixed fractions. Enter the whole number, numerator, and denominator for each fraction, select your desired operation, and click "Calculate".

Fraction 1

Whole Number: Numerator: Denominator:

Operation

Add (+) Subtract (-) Multiply (*) Divide (/)

Fraction 2

Whole Number: Numerator: Denominator:

Result:

Understanding Mixed Fractions

A mixed fraction is a number consisting of a whole number and a proper fraction. For example, 3 1/2 means three whole units plus one-half of another unit. They are commonly used in everyday life, such as in cooking recipes (e.g., "add 2 1/4 cups of flour") or measurements.

Converting Mixed Fractions to Improper Fractions

Before performing arithmetic operations, it's often easiest to convert mixed fractions into improper fractions. An improper fraction is one where the numerator is greater than or equal to the denominator (e.g., 7/2). To convert a mixed fraction W N/D (Whole, Numerator, Denominator) to an improper fraction:

Improper Numerator = (Whole Number × Denominator) + Numerator

Improper Denominator = Denominator

So, 3 1/2 becomes (3 × 2 + 1) / 2 = 7/2.

Performing Operations on Fractions

Addition and Subtraction

To add or subtract fractions, they must have a common denominator. If they don't, find the least common multiple (LCM) of the denominators and convert both fractions to equivalent fractions with that common denominator. Then, add or subtract the numerators and keep the common denominator.

Example: 1/2 + 1/3. The LCM of 2 and 3 is 6. So, 3/6 + 2/6 = 5/6.

Multiplication

To multiply fractions, simply multiply the numerators together and multiply the denominators together.

Example: 1/2 × 1/3 = (1 × 1) / (2 × 3) = 1/6.

Division

To divide fractions, you "flip" the second fraction (find its reciprocal) and then multiply.

Example: 1/2 ÷ 1/3 = 1/2 × 3/1 = (1 × 3) / (2 × 1) = 3/2.

Simplifying and Converting Back to Mixed Fractions

After performing an operation, the resulting improper fraction should ideally be simplified and converted back to a mixed fraction if applicable.

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. For example, 6/8 simplifies to 3/4 (GCD is 2).

To convert an improper fraction N/D back to a mixed fraction:

Whole Number = Integer part of (N ÷ D)

New Numerator = Remainder of (N ÷ D)

Denominator = Original Denominator

Example: 7/2 becomes 3 1/2 (7 divided by 2 is 3 with a remainder of 1).

Example Calculation: Adding Mixed Fractions

Let's add 1 1/2 and 2 1/3:

Convert to improper fractions:
- 1 1/2 = (1 × 2 + 1) / 2 = 3/2
- 2 1/3 = (2 × 3 + 1) / 3 = 7/3
Find a common denominator (LCM of 2 and 3 is 6):
- 3/2 = 9/6
- 7/3 = 14/6
Add the fractions:
- 9/6 + 14/6 = 23/6
Convert back to a mixed fraction:
- 23 ÷ 6 = 3 with a remainder of 5.
- So, 23/6 = 3 5/6.

The calculator above automates these steps for you, providing quick and accurate results for any mixed fraction operation.

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} .calculator-article code { background-color: #e9ecef; padding: 2px 4px; border-radius: 4px; font-family: 'Courier New', Courier, monospace; } @media (max-width: 600px) { .calculator-container { flex-direction: column; align-items: center; } .input-group { width: 100%; max-width: 250px; } .input-group input[type="number"], .input-group select { width: 100%; } } // Function to find the Greatest Common Divisor (GCD) 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 to convert a mixed fraction (W N/D) to an improper fraction (N'/D') function mixedToImproper(whole, num, den) { if (den === 0) { return { numerator: 0, denominator: 0 }; // Indicate error } var sign = 1; if (whole < 0) { sign = -1; whole = Math.abs(whole); } var improperNum = (whole * den) + num; return { numerator: sign * improperNum, denominator: den }; } // Function to convert an improper fraction (N/D) to a simplified mixed fraction string function improperToMixedString(num, den) { if (den === 0) { return "Undefined (Division by Zero)"; } if (num === 0) { return "0"; } var sign = ""; if (num < 0) { sign = "-"; num = Math.abs(num); } var commonDivisor = gcd(num, den); num /= commonDivisor; den /= commonDivisor; var whole = Math.floor(num / den); var remainder = num % den; if (remainder === 0) { return sign + whole.toString(); } else if (whole === 0) { return sign + remainder.toString() + "/" + den.toString(); } else { return sign + whole.toString() + " " + remainder.toString() + "/" + den.toString(); } } function calculateMixedFractions() { var whole1 = parseFloat(document.getElementById("whole1").value); var num1 = parseFloat(document.getElementById("num1").value); var den1 = parseFloat(document.getElementById("den1").value); var operation = document.getElementById("operation").value; var whole2 = parseFloat(document.getElementById("whole2").value); var num2 = parseFloat(document.getElementById("num2").value); var den2 = parseFloat(document.getElementById("den2").value); var resultDiv = document.getElementById("result"); // Input validation if (isNaN(whole1) || isNaN(num1) || isNaN(den1) || isNaN(whole2) || isNaN(num2) || isNaN(den2)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (den1 === 0 || den2 === 0) { resultDiv.innerHTML = "Denominator cannot be zero."; return; } if (num1 < 0 || num2 < 0) { resultDiv.innerHTML = "Numerators for the fractional part should be non-negative."; return; } if (den1 < 1 || den2 < 1) { resultDiv.innerHTML = "Denominators must be positive integers."; return; } // Convert mixed fractions to improper fractions var frac1 = mixedToImproper(whole1, num1, den1); var frac2 = mixedToImproper(whole2, num2, den2); var resultNum; var resultDen; switch (operation) { case "add": resultNum = (frac1.numerator * frac2.denominator) + (frac2.numerator * frac1.denominator); resultDen = frac1.denominator * frac2.denominator; break; case "subtract": resultNum = (frac1.numerator * frac2.denominator) – (frac2.numerator * frac1.denominator); resultDen = frac1.denominator * frac2.denominator; break; case "multiply": resultNum = frac1.numerator * frac2.numerator; resultDen = frac1.denominator * frac2.denominator; break; case "divide": if (frac2.numerator === 0) { resultDiv.innerHTML = "Cannot divide by zero."; return; } resultNum = frac1.numerator * frac2.denominator; resultDen = frac1.denominator * frac2.numerator; break; default: resultDiv.innerHTML = "Invalid operation selected."; return; } resultDiv.innerHTML = improperToMixedString(resultNum, resultDen); } // Initial calculation on page load (optional, but good for showing an example) document.addEventListener('DOMContentLoaded', function() { calculateMixedFractions(); });