Perform addition, subtraction, multiplication, and division on fractions, similar to the iPhone calculator.
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Result: N/A
Understanding and Using the Fraction Calculator
The iPhone's native calculator app, while powerful, doesn't always display fractions in a way that's easy to manipulate directly for complex operations. This specialized calculator is designed to bridge that gap, allowing you to input two fractions and perform the four basic arithmetic operations: addition, subtraction, multiplication, and division. Understanding how these operations work is key to using this tool effectively and for general mathematical proficiency.
How Fractions Work
A fraction represents a part of a whole. It consists of two numbers:
Numerator: The top number, indicating how many parts you have.
Denominator: The bottom number, indicating the total number of equal parts the whole is divided into.
For example, in the fraction 1/2, '1' is the numerator and '2' is the denominator. It means you have one part out of two equal parts that make up a whole.
Fraction Arithmetic Operations
This calculator handles the following operations:
1. Addition and Subtraction:
To add or subtract fractions, they must have a common denominator. If they don't, you need to find the least common multiple (LCM) of the denominators and adjust the numerators accordingly.
Formula:
Addition: (a/b) + (c/d) = (ad + bc) / bd
Subtraction: (a/b) – (c/d) = (ad – bc) / bd
Note: For optimal results and simpler calculations, finding the LCM first can lead to a simplified final fraction directly. This calculator uses the 'bd' approach for simplicity in direct calculation, and a simplification step is applied afterwards.
2. Multiplication:
Multiplying fractions is straightforward. You multiply the numerators together and the denominators together.
Formula:
(a/b) * (c/d) = ac / bd
3. Division:
To divide fractions, you invert the second fraction (turn it upside down, making it a reciprocal) and then multiply.
Formula:
(a/b) / (c/d) = (a/b) * (d/c) = ad / bc
Simplifying Fractions
After performing an operation, the resulting fraction might not be in its simplest form. Simplifying a fraction means dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, 4/8 can be simplified to 1/2 because the GCD of 4 and 8 is 4.
Using the Calculator
Enter the numerator and denominator for the first fraction.
Enter the numerator and denominator for the second fraction.
Select the operation you wish to perform (Add, Subtract, Multiply, Divide).
The result will be displayed, simplified to its lowest terms.
Example Calculation (Addition)
Let's add 1/2 and 3/4:
First Fraction: Numerator = 1, Denominator = 2
Second Fraction: Numerator = 3, Denominator = 4
Operation: Add (+)
Using the formula: (1/2) + (3/4) = (1*4 + 3*2) / (2*4) = (4 + 6) / 8 = 10/8.
Simplifying 10/8 by dividing both by their GCD (which is 2): 10 ÷ 2 / 8 ÷ 2 = 5/4.
The calculator will output 5/4.
Use Cases
This calculator is useful for:
Students learning fraction arithmetic.
Quick calculations in cooking or DIY projects where measurements are fractional.
Anyone needing to precisely combine or divide fractional quantities.
Verifying results obtained from other calculation methods.
function gcd(a, b) {
var a = Math.abs(a);
var b = Math.abs(b);
while(b) {
var t = b;
b = a % b;
a = t;
}
return a;
}
function simplifyFraction(num, den) {
if (den === 0) return "Undefined (division by zero)";
if (num === 0) return "0/1";
var commonDivisor = gcd(num, den);
num /= commonDivisor;
den /= commonDivisor;
// Ensure denominator is positive
if (den = Math.abs(den)) {
// var whole = Math.floor(num / den);
// num = num % den;
// if (num === 0) return whole + "/1″; // Or just whole
// return whole + " " + num + "/" + den;
// }
return num + "/" + den;
}
function calculateFraction(operation) {
var num1Input = document.getElementById("num1");
var den1Input = document.getElementById("den1");
var num2Input = document.getElementById("num2");
var den2Input = document.getElementById("den2");
var resultDiv = document.getElementById("result").querySelector("span");
var num1 = parseFloat(num1Input.value);
var den1 = parseFloat(den1Input.value);
var num2 = parseFloat(num2Input.value);
var den2 = parseFloat(den2Input.value);
// Input validation
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDiv.textContent = "Invalid input. Please enter numbers.";
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.textContent = "Undefined (denominator cannot be zero).";
return;
}
var resultNum, resultDen;
switch(operation) {
case '+':
resultNum = num1 * den2 + num2 * den1;
resultDen = den1 * den2;
break;
case '-':
resultNum = num1 * den2 – num2 * den1;
resultDen = den1 * den2;
break;
case '*':
resultNum = num1 * num2;
resultDen = den1 * den2;
break;
case '/':
if (num2 === 0) {
resultDiv.textContent = "Undefined (division by zero).";
return;
}
resultNum = num1 * den2;
resultDen = den1 * num2;
break;
default:
resultDiv.textContent = "Unknown operation.";
return;
}
var simplifiedResult = simplifyFraction(resultNum, resultDen);
resultDiv.textContent = simplifiedResult;
}