Fraction Calculator

Add, subtract, multiply, and divide fractions. Simplify fractions, convert between mixed numbers and improper fractions.

Operation

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First Fraction

Numerator

Denominator

Second Fraction

Numerator

Denominator

About Fraction Calculator

What Are Fractions?

A fraction represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). The denominator tells you how many equal parts the whole is divided into, while the numerator tells you how many of those parts you have. For example, 3/4 means 3 out of 4 equal parts.

Fractions can also be expressed as mixed numbers, which combine a whole number with a proper fraction (e.g., 2 3/4). Any mixed number can be converted to an improper fraction and vice versa.

Fraction Operations

Addition & Subtraction: To add or subtract fractions, you need a common denominator. Find the least common multiple (LCM) of the denominators, convert each fraction, then add or subtract the numerators.

Multiplication: Multiply the numerators together and multiply the denominators together. Simplify the result by dividing both parts by their greatest common divisor (GCD).

Division: Flip the second fraction (take its reciprocal) and then multiply. For example, 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12 = 5/6.

Simplifying Fractions

Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD can be found using the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero.

A fraction is fully simplified when the only common factor of the numerator and denominator is 1. For example, 24/36 simplifies to 2/3 because the GCD of 24 and 36 is 12.

Real-World Uses of Fractions

Fractions are used everywhere in daily life. In cooking, recipes call for fractional measurements like 1/2 cup or 3/4 teaspoon. In construction, dimensions are often expressed in fractions of an inch. Financial calculations use fractions when splitting costs or calculating interest rates.

In science and engineering, fractions help express ratios, probabilities, and proportions. Understanding fractions is also foundational for learning algebra, calculus, and other advanced mathematics.

Frequently Asked Questions

How do I add fractions with different denominators?

To add fractions with different denominators, first find the least common denominator (LCD) by determining the least common multiple of the two denominators. Then convert each fraction so that it uses the LCD as its denominator. Finally, add the numerators and keep the common denominator. Simplify the result if possible.

What is the difference between a proper and an improper fraction?

A proper fraction has a numerator smaller than its denominator (e.g., 3/4), so its value is less than 1. An improper fraction has a numerator equal to or greater than its denominator (e.g., 7/4), meaning its value is 1 or greater. Improper fractions can be converted to mixed numbers.

How do I simplify a fraction?

To simplify (or reduce) a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 12/18 simplifies to 2/3 because the GCD of 12 and 18 is 6.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator. Place that result over the original denominator. For example, 2 3/4 becomes (2 × 4 + 3)/4 = 11/4.

Why do I flip the second fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a/b is b/a. So a/b ÷ c/d becomes a/b × d/c. This rule follows from the mathematical definition of division.

Can fractions have negative numbers?

Yes. A fraction is negative when exactly one of the numerator or denominator is negative. Writing −3/4, 3/−4, or −(3/4) are all equivalent. If both the numerator and denominator are negative, the fraction is positive.

Additional Resources

Khan Academy – Fractions Math is Fun – Fractions Purplemath – Fractions Review

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