Fractions are a fundamental concept in mathematics, representing a part of a whole. They consist of two numbers: a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar. The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.
Basic Operations with Fractions
This calculator helps you perform the four basic arithmetic operations on two fractions:
1. Addition and Subtraction
To add or subtract fractions, they must have a common denominator. If they already share a denominator, you simply add or subtract the numerators and keep the common denominator:
(a/b) + (c/b) = (a+c)/b(a/b) - (c/b) = (a-c)/b
If the denominators are different, you need to find a common denominator, typically the least common multiple (LCM) of the two denominators. Then, you adjust the numerators accordingly and perform the addition or subtraction:
(a/b) + (c/d) = (ad + bc) / bd(a/b) - (c/d) = (ad - bc) / bd
2. Multiplication
Multiplying fractions is straightforward. You multiply the numerators together and the denominators together:
(a/b) * (c/d) = (a * c) / (b * d)
Simplification can be done before or after multiplication.
3. Division
To divide one fraction by another, you invert the second fraction (its reciprocal) and then multiply:
(a/b) รท (c/d) = (a/b) * (d/c) = (a * d) / (b * c)
It's crucial that the denominator of the divisor (the second fraction) is not zero, and also that the numerator of the divisor is not zero if you are dividing by it.
Simplifying Fractions
After performing an operation, the resulting fraction is often simplified to its lowest terms. This is done by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it. For example, 4/8 simplifies to 1/2 because the GCD of 4 and 8 is 4.
Use Cases for Fraction Arithmetic
Cooking and Recipes: Scaling recipes up or down often involves fractional amounts.
Engineering and Construction: Measuring and dividing materials, calculating ratios.
Finance: While decimals are more common, understanding fractional growth or risk can be helpful.
Science: Representing proportions, rates, and dilutions.
Everyday Measurements: Dividing resources, sharing items, or understanding parts of a whole.
This calculator provides a quick and accurate way to handle these calculations, ensuring precision in various applications.
var currentOperation = '+'; // Default operation
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 simplifyFraction(numerator, denominator) {
if (denominator === 0) {
return { numerator: NaN, denominator: NaN }; // Indicate error
}
if (numerator === 0) {
return { numerator: 0, denominator: 1 };
}
var commonDivisor = gcd(numerator, denominator);
numerator /= commonDivisor;
denominator /= commonDivisor;
// Ensure denominator is positive
if (denominator 0) {
buttons[0].classList.add('active'); // Assumes '+' is the first button
}
});