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What is a Fraction in Mathematics?

A fraction represents a numerical ratio expressing a portion of a whole quantity. It consists of a top number called the numerator (which indicates how many equal parts are selected) and a bottom non-zero number called the denominator (which defines the total number of equal parts that form a complete unit).

Standard Fraction Operation Formulas

Our fraction calculator processes standard arithmetic operations using exact algebraic fraction rules:

Simplifying Fractions & Mixed Numbers

After performing an operation, fractions are simplified by dividing the numerator and denominator by their Greatest Common Divisor (GCD). If the resulting improper fraction has a numerator larger than its denominator, it can be converted into a mixed number containing a whole integer and a proper fraction.

Frequently Asked Questions (FAQs)

1. How do you add or subtract fractions with different denominators?

Find a common denominator (the product of denominators or Least Common Multiple), convert each fraction into an equivalent fraction with that common denominator, and then add or subtract the numerators while keeping the denominator constant.

2. How do you multiply and divide fractions?

To multiply fractions, multiply the top numbers together and bottom numbers together. To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction.

3. What is a simplified or reduced fraction?

A fraction is in its simplest form when the numerator and denominator share no common factors other than 1.