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Fraction Calculator

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Decimal format: 0

How to Use the Fraction Calculator

This tool automatically adds, subtracts, multiplies, or divides fractions and returns the answer in its simplest, reduced form.

  1. Enter Fraction 1: Type the numerator (top number) and denominator (bottom number) into the first stack of boxes.
  2. Select Operation: Choose to add (+), subtract (−), multiply (×), or divide (÷) using the center dropdown menu.
  3. Enter Fraction 2: Type the values into the second stack of boxes.
  4. Calculate: Click the calculate button to see the simplified fraction and its decimal equivalent instantly.

How Fraction Math Works

A fraction represents a part of a whole or, more generally, any number of equal parts. Working with fractions can be tricky because the mathematical rules change entirely depending on whether you are adding, multiplying, or dividing.

1. Adding and Subtracting Fractions

To add or subtract fractions, you must first find a Common Denominator. The bottom numbers must match before you can combine the top numbers.

a⁄b + c⁄d = (ad + bc)⁄bd

Example: To add 1/2 and 1/3, you find a common denominator of 6. You convert them to 3/6 and 2/6. Then you add the numerators (3 + 2) to get 5/6.

2. Multiplying Fractions

Multiplying fractions is much more straightforward than adding them. You do not need a common denominator. You simply multiply the top numbers straight across, and then multiply the bottom numbers straight across.

a⁄b × c⁄d = (a × c)⁄(b × d)

3. Dividing Fractions

To divide fractions, you use a method often taught as "Keep, Change, Flip." You keep the first fraction the same, change the division sign to multiplication, and flip the second fraction upside down (creating its reciprocal). Then, you multiply straight across.

a⁄b ÷ c⁄d = a⁄b × d⁄c

Frequently Asked Questions (FAQ)

1. What is a simplified fraction?

A fraction is in its simplest form when the top and bottom numbers can no longer be divided evenly by the same whole number. For example, 4/8 simplifies down to 1/2 because both the 4 and the 8 can be divided by 4.

2. What is an improper fraction?

An improper fraction is a fraction where the numerator (top number) is larger than the denominator (bottom number), such as 5/4. This means the value is greater than 1. It can also be written as a mixed number (e.g., 1 ¼).

3. Can a denominator be zero?

No. In mathematics, dividing by zero is undefined. If you attempt to enter a zero in the bottom box of our calculator, it will return an error to protect the calculation.