Fraction Calculator

Working with fractions is a fundamental skill in mathematics. Our calculator is designed to simplify these operations, but understanding the process behind them is key to building your confidence. Below, we break down how each of the four basic arithmetic operations works with fractions, using examples to guide you.

Addition and Subtraction

To add or subtract fractions, they must share a common denominator. If they don’t, you first need to find the lowest common multiple (LCM) of the denominators. For example, to calculate 1/2 + 1/4, the LCM of 2 and 4 is 4. You would convert 1/2 to 2/4. Then, you simply add the numerators: 2/4 + 1/4 = 3/4. Subtraction follows the same principle; you just subtract the numerators instead.

Multiplication

Multiplying fractions is more straightforward. You multiply the numerators together to get the new numerator, and multiply the denominators together for the new denominator. For instance, (1/2) × (3/4) results in (1×3)/(2×4), which is 3/8. There is no need to find a common denominator, making multiplication one of the simpler fraction operations to perform manually.

Division

Dividing fractions involves an extra step. You must find the reciprocal of the second fraction (the one you are dividing by) and then multiply the first fraction by it. The reciprocal is found by simply inverting the fraction. For example, to calculate (1/2) ÷ (1/4), you first flip 1/4 to get 4/1. Then, you multiply: (1/2) × (4/1) = 4/2, which simplifies to 2. This method is often remembered by the phrase "invert and multiply".