Fraction Calculator

What Is a Fraction?

A fraction represents a part of a whole, written as one number over another separated by a line. The top number (numerator) tells you how many parts you have, and the bottom number (denominator) tells you how many equal parts the whole is divided into. The fraction 3/4 means three out of four equal parts. Fractions are fundamental to mathematics, cooking, construction, music, and countless everyday situations where quantities need to be divided into parts smaller than whole numbers.

How to Add and Subtract Fractions?

To add or subtract fractions with the same denominator, simply add or subtract the numerators and keep the denominator: 2/7 + 3/7 = 5/7. When denominators differ, you must find a common denominator first. To add 1/3 + 1/4, convert both to twelfths: 4/12 + 3/12 = 7/12. The easiest way to find a common denominator is to multiply the two denominators together, though the least common multiple produces smaller numbers. Enter your fractions in the calculator above and the tool handles common denominators, computation, and simplification automatically.

How to Multiply and Divide Fractions?

Multiplying fractions is simpler than adding them: multiply the numerators together and the denominators together. 2/3 times 4/5 = 8/15. No common denominator is needed. Dividing fractions uses the "flip and multiply" method: to divide by a fraction, flip it (swap numerator and denominator) and multiply. 2/3 divided by 4/5 becomes 2/3 times 5/4 = 10/12, which simplifies to 5/6. This shortcut works because dividing by a fraction is the same as multiplying by its reciprocal.

How to Simplify a Fraction?

Simplifying (or reducing) a fraction means finding the smallest equivalent fraction. Divide both the numerator and denominator by their greatest common factor (GCF). The fraction 12/18 has a GCF of 6, so 12/18 simplifies to 2/3. The fraction 8/20 has a GCF of 4, so it simplifies to 2/5. A fraction is fully simplified when no number other than 1 divides evenly into both the numerator and denominator. The calculator automatically simplifies every result to its lowest terms.

How to Convert Fractions to Decimals and Percentages?

To convert a fraction to a decimal, divide the numerator by the denominator. 3/4 = 0.75. 1/3 = 0.3333 (repeating). 5/8 = 0.625. To convert a fraction to a percentage, divide and multiply by 100. 3/4 = 75%. 2/5 = 40%. 7/8 = 87.5%. To convert a decimal back to a fraction, place it over the appropriate power of 10 and simplify. 0.6 = 6/10 = 3/5. 0.125 = 125/1000 = 1/8. These conversions appear constantly in school math, standardized tests, cooking measurements, and financial calculations.

Mixed Numbers and Improper Fractions

A mixed number combines a whole number with a fraction: 2 and 3/4. An improper fraction has a numerator larger than its denominator: 11/4. They represent the same value. To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place over the original denominator: 2 and 3/4 = (2 times 4 + 3)/4 = 11/4. To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator: 11/4 = 2 remainder 3 = 2 and 3/4.

Fractions in Everyday Life

Cooking relies heavily on fractions. Doubling a recipe that calls for 3/4 cup of flour requires knowing that 3/4 + 3/4 = 1 and 1/2 cups. Construction measurements use fractions of inches: a board might need to be cut at 5 and 3/8 inches. Music divides time into fractions: quarter notes, eighth notes, sixteenth notes. Stock markets historically quoted prices in fractions (now decimalized). Pizza is divided into fractional slices. Understanding fractions is not optional for functioning in a world that constantly divides things into parts.

Common Fraction Equivalents

Memorizing common fraction-decimal equivalents speeds up everyday calculations. 1/2 = 0.5, 1/3 = 0.333, 2/3 = 0.667, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875, 1/10 = 0.1, 1/16 = 0.0625. Construction workers memorize sixteenths for tape measure readings. Cooks memorize thirds and quarters for recipe scaling. Financial analysts use fractions when working with historical stock prices and bond calculations that predate decimal quotation systems.

Frequently asked questions