Fractions are a fundamental concept in mathematics, representing a part of a whole. They are expressed as a ratio of two integers, a numerator (the number above the line) and a denominator (the number below the line). For example, in the fraction 1/2, 1 is the numerator and 2 is the denominator.
This calculator is designed to help you perform basic arithmetic operations (addition, subtraction, multiplication, and division) on two fractions. Understanding these operations is crucial in various fields, from everyday cooking and DIY projects to advanced engineering and scientific research.
How Fractions Work
Numerator: Indicates how many parts of the whole are being considered.
Denominator: Indicates the total number of equal parts the whole is divided into. The denominator cannot be zero.
Mathematical Operations Explained
Let's consider two fractions: a/b and c/d.
1. Addition (a/b + c/d)
To add fractions, they must have a common denominator. If they don't, we find the least common multiple (LCM) of the denominators (b and d). The formula is:
(a*d + c*b) / (b*d)
The result can often be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
2. Subtraction (a/b - c/d)
Similar to addition, fractions need a common denominator. The formula is:
(a*d - c*b) / (b*d)
Again, simplify the result if possible using the GCD.
3. Multiplication (a/b * c/d)
Multiplying fractions is straightforward. You multiply the numerators together and the denominators together:
(a*c) / (b*d)
Simplification is also recommended here.
4. Division (a/b รท c/d)
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of c/d is d/c. The formula is:
a/b * d/c = (a*d) / (b*c)
Note that the denominator of the second fraction (d) becomes part of the numerator in the calculation, and the numerator of the second fraction (c) becomes part of the denominator. Ensure c is not zero.
Simplifying Fractions (GCD)
To simplify a fraction, find the greatest common divisor (GCD) of its numerator and denominator and divide both by it. For example, to simplify 4/8, the GCD of 4 and 8 is 4. Dividing both by 4 gives 1/2.
Use Cases
Baking and Cooking: Adjusting recipe quantities (e.g., doubling or halving a recipe that calls for 3/4 cup of flour).
Construction and DIY: Measuring and cutting materials accurately.
Finance: Calculating proportions, discounts, or interest rates expressed as fractions.
Science and Engineering: Performing calculations involving ratios and proportions.
Education: Learning and practicing fundamental arithmetic skills.
This calculator simplifies these common tasks, providing quick and accurate results for your fraction arithmetic needs.
function gcd(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
var t = b;
b = a % b;
a = t;
}
return a;
}
function calculateFraction() {
var num1 = parseInt(document.getElementById("numerator1").value);
var den1 = parseInt(document.getElementById("denominator1").value);
var num2 = parseInt(document.getElementById("numerator2").value);
var den2 = parseInt(document.getElementById("denominator2").value);
var operation = document.getElementById("operation").value;
var resultDisplay = document.getElementById("result-value");
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDisplay.innerText = "Please enter valid numbers for all inputs.";
return;
}
if (den1 === 0 || den2 === 0) {
resultDisplay.innerText = "Denominator cannot be zero.";
return;
}
if (operation === 'divide' && num2 === 0) {
resultDisplay.innerText = "Cannot divide by zero.";
return;
}
var resultNum, resultDen;
switch (operation) {
case "add":
resultNum = (num1 * den2) + (num2 * den1);
resultDen = den1 * den2;
break;
case "subtract":
resultNum = (num1 * den2) – (num2 * den1);
resultDen = den1 * den2;
break;
case "multiply":
resultNum = num1 * num2;
resultDen = den1 * den2;
break;
case "divide":
resultNum = num1 * den2;
resultDen = den1 * num2;
break;
default:
resultDisplay.innerText = "Invalid operation selected.";
return;
}
// Simplify the fraction
var commonDivisor = gcd(resultNum, resultDen);
resultNum = resultNum / commonDivisor;
resultDen = resultDen / commonDivisor;
// Handle negative denominator by moving the sign to the numerator
if (resultDen < 0) {
resultNum = -resultNum;
resultDen = -resultDen;
}
// Display the result
if (resultDen === 1) {
resultDisplay.innerText = resultNum.toString();
} else {
resultDisplay.innerText = resultNum + "/" + resultDen;
}
}