Mixed numbers consist of a whole number and a proper fraction. To add, subtract, multiply, or divide them, follow these professional steps:
Step 1: Convert to Improper Fractions. Multiply the whole number by the denominator and add the numerator. Place this over the original denominator.
Step 2: Find a Common Denominator (for +/-). If adding or subtracting, ensure both fractions have the same bottom number.
Step 3: Perform the Math. Execute the operation on the numerators while keeping the common denominator (or multiplying across for products).
Step 4: Simplify and Convert Back. Reduce the fraction to its lowest terms and convert it back into a mixed number format.
Real-World Example
Imagine you are baking and need to combine 1 ½ cups of flour with 2 ¾ cups of flour:
Convert 1 ½ to 3/2 and 2 ¾ to 11/4.
Find a common denominator: 3/2 becomes 6/4.
Add: 6/4 + 11/4 = 17/4.
Convert back: 17 ÷ 4 = 4 with a remainder of 1.
Result: 4 ¼ cups.
Why Accuracy Matters
Using a mixed number calculator is essential for precision in construction, woodworking, and culinary arts where measurements are rarely simple integers. Our tool ensures your calculations are simplified to the lowest possible denominator automatically.
function gcd(a, b) {
return b ? gcd(b, a % b) : Math.abs(a);
}
function calculateMixedFractions() {
var w1 = parseInt(document.getElementById('w1').value) || 0;
var n1 = parseInt(document.getElementById('n1').value) || 0;
var d1 = parseInt(document.getElementById('d1').value) || 1;
var w2 = parseInt(document.getElementById('w2').value) || 0;
var n2 = parseInt(document.getElementById('n2').value) || 0;
var d2 = parseInt(document.getElementById('d2').value) || 1;
var op = document.getElementById('operation').value;
if (d1 === 0 || d2 === 0) {
alert("Denominator cannot be zero.");
return;
}
// Convert to improper fractions
// (Whole * Denom + Num) / Denom
// Handle negative whole numbers correctly
var sign1 = (w1 < 0) ? -1 : 1;
var sign2 = (w2 < 0) ? -1 : 1;
var imp_n1 = (Math.abs(w1) * d1 + n1) * sign1;
var imp_d1 = d1;
var imp_n2 = (Math.abs(w2) * d2 + n2) * sign2;
var imp_d2 = d2;
var res_n, res_d;
if (op === "add") {
res_n = (imp_n1 * imp_d2) + (imp_n2 * imp_d1);
res_d = imp_d1 * imp_d2;
} else if (op === "subtract") {
res_n = (imp_n1 * imp_d2) – (imp_n2 * imp_d1);
res_d = imp_d1 * imp_d2;
} else if (op === "multiply") {
res_n = imp_n1 * imp_n2;
res_d = imp_d1 * imp_d2;
} else if (op === "divide") {
if (imp_n2 === 0) {
alert("Cannot divide by zero.");
return;
}
res_n = imp_n1 * imp_d2;
res_d = imp_d1 * imp_n2;
}
// Simplify the fraction
var common = gcd(res_n, res_d);
res_n = res_n / common;
res_d = res_d / common;
// Handle negative signs in denominator
if (res_d = res_d) {
final_whole = (res_n > 0) ? Math.floor(res_n / res_d) : Math.ceil(res_n / res_d);
final_num = Math.abs(res_n % res_d);
}
var resultText = "";
if (final_whole !== 0) {
resultText += final_whole;
if (final_num !== 0) resultText += " " + final_num + "/" + final_den;
} else if (final_num === 0) {
resultText = "0";
} else {
resultText = (res_n < 0 ? "-" : "") + final_num + "/" + final_den;
}
document.getElementById('fractionOutput').innerHTML = "Result: " + resultText;
document.getElementById('improperOutput').innerHTML = "Improper fraction: " + res_n + "/" + res_d;
document.getElementById('fractionResultBox').style.display = "block";
}