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Fraction Calculator

Add, subtract, multiply or divide fractions with automatic simplification.


Fractions in Mathematics

In mathematics, a fraction represents a part of a whole. Every fraction consists of two numbers: a numerator and a denominator. The numerator shows how many parts are taken, while the denominator shows how many equal parts make up the whole.

A fraction is undefined if its denominator is zero, since division by zero is not mathematically valid.

Understanding Numerator and Denominator

The numerator counts selected parts of a whole, while the denominator represents the total number of equal parts. For example, in the fraction 3/8, three parts are taken from a whole divided into eight equal parts.

Fractions in Real Life

Fractions are commonly illustrated using everyday examples, such as slicing a pie into equal pieces. If three slices are eaten from eight, the remaining fraction is 5/8.

Adding Fractions

To add fractions, a common denominator is required. Once the denominators match, the numerators can be added directly.

a/b + c/d = (ad + bc) / bd

Example: 3/4 + 1/6 = 11/12

A common denominator can be found either by multiplying denominators or by using the least common multiple (LCM).

Subtracting Fractions

Fraction subtraction follows the same rules as addition. Both fractions must share a common denominator before subtracting the numerators.

a/b − c/d = (ad − bc) / bd

Example: 3/4 − 1/6 = 7/12

Multiplying Fractions

Multiplying fractions does not require a common denominator. Simply multiply the numerators together and the denominators together.

a/b × c/d = ac / bd

Example: 3/4 × 1/6 = 1/8

Dividing Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. The reciprocal is formed by switching the numerator and denominator.

a/b ÷ c/d = a/b × d/c = ad / bc

Example: 3/4 ÷ 1/6 = 9/2

Simplifying Fractions

Simplified fractions are easier to work with and understand. A fraction is simplified by dividing both the numerator and denominator by their greatest common factor (GCF).

For example, 220/440 simplifies to 1/2 by dividing both values by 220.

Converting Between Fractions and Decimals

Converting decimals to fractions involves recognizing place values as powers of ten. For example, 0.1234 becomes 1234/10000, which can then be simplified.

Fractions with denominators of 10, 100, or 1000 can be converted to decimals directly. Other fractions require long division.

Frequently Asked Questions

Can a fraction have a denominator of zero?

No. A denominator of zero makes a fraction undefined.

Is using LCM always better for addition?

Using the least common multiple is often more efficient and usually results in a simplified answer.

What is a mixed number?

A mixed number combines a whole number with a proper fraction, such as 2 1/3.

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