Mixed Fraction Calculator

Mixed Fraction 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




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

Fraction 2




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 toImproper(whole, num, den) { if (isNaN(whole) || isNaN(num) || isNaN(den)) { return { error: "Invalid input: Please enter numbers for all fields." }; } if (den === 0) { return { error: "Denominator cannot be zero." }; } if (num < 0) { return { error: "Numerator must be non-negative for mixed fraction input." }; } if (den < 1) { return { error: "Denominator must be a positive number." }; } var improperNum; if (whole < 0) { improperNum = -(Math.abs(whole) * den + num); } else { improperNum = whole * den + num; } return { numerator: improperNum, denominator: den }; } function toMixed(numerator, denominator) { if (denominator === 0) { return { error: "Denominator cannot be zero in the result." }; } if (numerator === 0) { return { whole: 0, numerator: 0, denominator: 1 }; } var isNegative = (numerator 0) || (numerator > 0 && denominator < 0); var absNum = Math.abs(numerator); var absDen = Math.abs(denominator); var commonDivisor = gcd(absNum, absDen); var simplifiedNum = absNum / commonDivisor; var simplifiedDen = absDen / commonDivisor; var whole = Math.floor(simplifiedNum / simplifiedDen); var remainderNum = simplifiedNum % simplifiedDen; if (isNegative) { whole = -whole; } return { whole: whole, numerator: remainderNum, denominator: simplifiedDen }; } function calculateMixedFractions() { var whole1 = parseInt(document.getElementById("whole1").value); var num1 = parseInt(document.getElementById("num1").value); var den1 = parseInt(document.getElementById("den1").value); var whole2 = parseInt(document.getElementById("whole2").value); var num2 = parseInt(document.getElementById("num2").value); var den2 = parseInt(document.getElementById("den2").value); var operation = document.getElementById("operation").value; var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; var frac1 = toImproper(whole1, num1, den1); if (frac1.error) { resultDiv.innerHTML = "" + frac1.error + ""; return; } var frac2 = toImproper(whole2, num2, den2); if (frac2.error) { resultDiv.innerHTML = "" + frac2.error + ""; return; } var resultNum, 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; } var finalMixed = toMixed(resultNum, resultDen); if (finalMixed.error) { resultDiv.innerHTML = "" + finalMixed.error + ""; return; } var output = "Result: "; if (finalMixed.whole === 0 && finalMixed.numerator === 0) { output += "0"; } else if (finalMixed.whole === 0) { output += finalMixed.numerator + "/" + finalMixed.denominator; } else if (finalMixed.numerator === 0) { output += finalMixed.whole; } else { output += finalMixed.whole + " " + finalMixed.numerator + "/" + finalMixed.denominator; } var commonDivisorImproper = gcd(resultNum, resultDen); var simplifiedImproperNum = resultNum / commonDivisorImproper; var simplifiedImproperDen = resultDen / commonDivisorImproper; output += " (or " + simplifiedImproperNum + "/" + simplifiedImproperDen + " as an improper fraction)"; resultDiv.innerHTML = output; }

Understanding Mixed Fractions and Their Operations

A mixed fraction combines a whole number and a proper fraction (where the numerator is smaller than the denominator). For example, 2 1/2 means two whole units plus one-half of another unit. Mixed fractions are often used when a quantity is greater than one but not a whole number.

Components of a Mixed Fraction

  • Whole Number: The integer part of the mixed fraction (e.g., 2 in 2 1/2).
  • Numerator: The top number of the fractional part, indicating how many parts of the whole are considered (e.g., 1 in 2 1/2).
  • Denominator: The bottom number of the fractional part, indicating how many equal parts make up the whole (e.g., 2 in 2 1/2).

Converting Mixed Fractions to Improper Fractions

Before performing most 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., 5/2).

Steps:

  1. Multiply the whole number by the denominator.
  2. Add the numerator to the result from step 1. This becomes the new numerator.
  3. Keep the original denominator.

Example: Convert 2 1/2 to an improper fraction.

  • Whole number (2) × Denominator (2) = 4
  • 4 + Numerator (1) = 5 (new numerator)
  • Keep the original denominator (2)
  • Result: 5/2

Converting Improper Fractions to Mixed Fractions

After performing operations, you'll often want to convert the resulting improper fraction back into a mixed fraction for clarity.

Steps:

  1. Divide the numerator by the denominator. The whole number part of the quotient is the new whole number.
  2. The remainder of the division becomes the new numerator.
  3. The denominator remains the same.
  4. Simplify the fractional part if possible by dividing both the numerator and denominator by their greatest common divisor (GCD).

Example: Convert 7/3 to a mixed fraction.

  • 7 ÷ 3 = 2 with a remainder of 1
  • Whole number = 2
  • New numerator = 1
  • Denominator = 3
  • Result: 2 1/3

Arithmetic Operations with Mixed Fractions

1. Adding Mixed Fractions

Steps:

  1. Convert both mixed fractions to improper fractions.
  2. Find a common denominator for the improper fractions.
  3. Add the numerators, keeping the common denominator.
  4. Simplify the resulting improper fraction and convert it back to a mixed fraction if desired.

Example: 1 1/2 + 2 3/4

  • Convert to improper: 1 1/2 = 3/2, 2 3/4 = 11/4
  • Common denominator (4): 3/2 = 6/4
  • Add: 6/4 + 11/4 = 17/4
  • Convert to mixed: 17/4 = 4 1/4

2. Subtracting Mixed Fractions

Steps:

  1. Convert both mixed fractions to improper fractions.
  2. Find a common denominator for the improper fractions.
  3. Subtract the numerators, keeping the common denominator.
  4. Simplify the resulting improper fraction and convert it back to a mixed fraction if desired.

Example: 3 1/3 - 1 1/2

  • Convert to improper: 3 1/3 = 10/3, 1 1/2 = 3/2
  • Common denominator (6): 10/3 = 20/6, 3/2 = 9/6
  • Subtract: 20/6 - 9/6 = 11/6
  • Convert to mixed: 11/6 = 1 5/6

3. Multiplying Mixed Fractions

Steps:

  1. Convert both mixed fractions to improper fractions.
  2. Multiply the numerators together to get the new numerator.
  3. Multiply the denominators together to get the new denominator.
  4. Simplify the resulting improper fraction and convert it back to a mixed fraction if desired. (You can often cross-cancel before multiplying to simplify earlier).

Example: 1 1/2 × 2 1/3

  • Convert to improper: 1 1/2 = 3/2, 2 1/3 = 7/3
  • Multiply: (3/2) × (7/3) = (3 × 7) / (2 × 3) = 21/6
  • Simplify and convert to mixed: 21/6 = 7/2 = 3 1/2

4. Dividing Mixed Fractions

Steps:

  1. Convert both mixed fractions to improper fractions.
  2. "Keep, Change, Flip": Keep the first fraction, change the division sign to multiplication, and flip (find the reciprocal of) the second fraction.
  3. Multiply the fractions as described above.
  4. Simplify the resulting improper fraction and convert it back to a mixed fraction if desired.

Example: 2 1/2 ÷ 1 1/4

  • Convert to improper: 2 1/2 = 5/2, 1 1/4 = 5/4
  • Keep, Change, Flip: 5/2 × 4/5
  • Multiply: (5 × 4) / (2 × 5) = 20/10
  • Simplify and convert to mixed: 20/10 = 2

How to Use This Calculator

  1. Enter Fraction 1: Input the whole number, numerator, and denominator for your first mixed fraction into the respective fields.
  2. Select Operation: Choose whether you want to add, subtract, multiply, or divide using the dropdown menu.
  3. Enter Fraction 2: Input the whole number, numerator, and denominator for your second mixed fraction.
  4. Click "Calculate": The calculator will instantly display the result as a simplified mixed fraction and its improper fraction equivalent.

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