Mixed Numbers Calculator

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Mixed Number 1: /

Operation: + – * /

Mixed Number 2: /

Result:

What are Mixed Numbers?

A mixed number is a combination of a whole number and a proper fraction. For example, 3 1/2 is a mixed number, where '3' is the whole number part and '1/2' is the fractional part. They are often used to represent quantities that are greater than one but not a whole number. Mixed numbers can also be negative, such as -2 3/4, which means -(2 + 3/4).

How to Use the Mixed Numbers Calculator

Our Mixed Numbers Calculator simplifies arithmetic operations on mixed numbers. Follow these steps:

Enter Mixed Number 1: Input the whole number, numerator, and denominator for your first mixed number. For example, for 3 1/2, enter '3' in the 'Whole' field, '1' in the 'Num' field, and '2' in the 'Den' field. If you have a simple fraction like 1/2, enter '0' for the 'Whole' number. You can also enter negative whole numbers (e.g., -2) for negative mixed numbers.
Select Operation: Choose the desired arithmetic operation (+, -, *, /) from the dropdown menu.
Enter Mixed Number 2: Input the whole number, numerator, and denominator for your second mixed number, following the same rules as for Mixed Number 1.
Calculate: Click the "Calculate" button to see the result.

The calculator will display the result as a simplified mixed number, a simple fraction, or a whole number.

Understanding Mixed Number Operations

1. Converting Mixed Numbers to Improper Fractions

Before performing most operations, it's often easiest to convert mixed numbers into improper fractions. An improper fraction has a numerator larger than or equal to its denominator (e.g., 7/2). The formula is:

Improper Numerator = (Absolute Whole Number × Denominator) + Numerator

Improper Denominator = Original Denominator

If the original mixed number was negative, the resulting improper fraction's numerator will also be negative.

Example: Convert 3 1/2 to an improper fraction.

(3 × 2) + 1 = 7

So, 3 1/2 becomes 7/2.

Example: Convert -2 3/4 to an improper fraction.

-( (2 × 4) + 3 ) = -11

So, -2 3/4 becomes -11/4.

2. Adding and Subtracting Mixed Numbers

To add or subtract mixed numbers, convert them to improper fractions first. Then, find a common denominator for the fractions, adjust their numerators, and perform the addition or subtraction. Finally, simplify the resulting fraction and convert it back to a mixed number.

Example (Addition): 1 1/2 + 2 1/3

Convert to improper fractions: 1 1/2 = 3/2, 2 1/3 = 7/3
Find common denominator (LCM of 2 and 3 is 6): 3/2 = 9/6, 7/3 = 14/6
Add: 9/6 + 14/6 = 23/6
Convert back to mixed number: 23/6 = 3 5/6

3. Multiplying Mixed Numbers

To multiply mixed numbers, convert them to improper fractions. Multiply the numerators together and the denominators together. Simplify the resulting fraction and convert it back to a mixed number if necessary.

Example (Multiplication): 1 1/2 × 2 1/3

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

4. Dividing Mixed Numbers

To divide mixed numbers, convert them to improper fractions. Then, invert the second fraction (the divisor) and multiply it by the first fraction. Simplify the result and convert it back to a mixed number.

Example (Division): 2 1/2 ÷ 1 1/4

Convert to improper fractions: 2 1/2 = 5/2, 1 1/4 = 5/4
Invert the second fraction and multiply: (5/2) ÷ (5/4) = (5/2) × (4/5)
Multiply: (5 × 4) / (2 × 5) = 20/10
Simplify and convert: 20/10 = 2

// Helper 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; } // Helper function to find the Least Common Multiple (LCM) function lcm(a, b) { if (a === 0 || b === 0) return 0; return Math.abs(a * b) / gcd(a, b); } // Converts a mixed number (whole, numerator, denominator) to an improper fraction (numerator, denominator) function mixedToImproper(whole, num, den) { // Handle negative whole numbers correctly: -3 1/2 is -(3 + 1/2) = -7/2 if (whole < 0) { return { num: whole * den – num, den: den }; } return { num: whole * den + num, den: den }; } // Converts an improper fraction (numerator, denominator) to its mixed number components // Returns { whole, num, den, isNegative } function improperToMixedComponents(numerator, denominator) { if (denominator === 0) { return { error: "Division by zero" }; } if (numerator === 0) { return { whole: 0, num: 0, den: 1, isNegative: false }; } var isNegative = (numerator < 0) !== (denominator < 0); var absNumerator = Math.abs(numerator); var absDenominator = Math.abs(denominator); var commonDivisor = gcd(absNumerator, absDenominator); absNumerator /= commonDivisor; absDenominator /= commonDivisor; var whole = Math.floor(absNumerator / absDenominator); var num = absNumerator % absDenominator; var den = absDenominator; return { whole: whole, num: num, den: den, isNegative: isNegative }; } // Main calculation function function calculateMixedNumbers() { // Get input values for Mixed Number 1 var whole1Str = document.getElementById("whole1").value; var num1Str = document.getElementById("num1").value; var den1Str = document.getElementById("den1").value; // Get input values for Mixed Number 2 var whole2Str = document.getElementById("whole2").value; var num2Str = document.getElementById("num2").value; var den2Str = document.getElementById("den2").value; var operation = document.getElementById("operation").value; // Validate inputs var whole1 = parseFloat(whole1Str); var num1 = parseFloat(num1Str); var den1 = parseFloat(den1Str); var whole2 = parseFloat(whole2Str); var num2 = parseFloat(num2Str); var den2 = parseFloat(den2Str); if (isNaN(whole1) || isNaN(num1) || isNaN(den1) || isNaN(whole2) || isNaN(num2) || isNaN(den2)) { document.getElementById("result").innerHTML = "Please enter valid numbers for all fields."; return; } // Denominators must be positive, numerators of fractional part must be non-negative. if (den1 <= 0 || den2 <= 0) { document.getElementById("result").innerHTML = "Denominator cannot be zero or negative."; return; } if (num1 < 0 || num2 < 0) { document.getElementById("result").innerHTML = "Numerator of the fractional part cannot be negative."; return; } // Convert mixed numbers to improper fractions var frac1 = mixedToImproper(whole1, num1, den1); var frac2 = mixedToImproper(whole2, num2, den2); var finalNum, finalDen; switch (operation) { case "add": var commonDen = lcm(frac1.den, frac2.den); finalNum = (frac1.num * (commonDen / frac1.den)) + (frac2.num * (commonDen / frac2.den)); finalDen = commonDen; break; case "subtract": var commonDen = lcm(frac1.den, frac2.den); finalNum = (frac1.num * (commonDen / frac1.den)) – (frac2.num * (commonDen / frac2.den)); finalDen = commonDen; break; case "multiply": finalNum = frac1.num * frac2.num; finalDen = frac1.den * frac2.den; break; case "divide": if (frac2.num === 0) { document.getElementById("result").innerHTML = "Cannot divide by zero."; return; } finalNum = frac1.num * frac2.den; finalDen = frac1.den * frac2.num; break; default: document.getElementById("result").innerHTML = "Invalid operation selected."; return; } // Convert the resulting improper fraction back to mixed number components var resultComponents = improperToMixedComponents(finalNum, finalDen); if (resultComponents.error) { document.getElementById("result").innerHTML = "" + resultComponents.error + ""; return; } // Format the result string var resultString = ""; var signPrefix = resultComponents.isNegative ? "-" : ""; if (resultComponents.whole === 0 && resultComponents.num === 0) { resultString = "0"; } else if (resultComponents.whole === 0) { // Pure fraction (e.g., 1/2 or -1/2) resultString = signPrefix + resultComponents.num + "/" + resultComponents.den; } else if (resultComponents.num === 0) { // Pure whole number (e.g., 3 or -3) resultString = signPrefix + resultComponents.whole; } else { // Mixed number (e.g., 3 1/2 or -3 1/2) resultString = signPrefix + resultComponents.whole + " " + resultComponents.num + "/" + resultComponents.den; } document.getElementById("result").innerHTML = "

Result: " + resultString + "

"; }