Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.
Use this calculator if the numerators or denominators are very big integers.
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
A common, vulgar, or simple fraction consists of a numerator displayed above a line (or before a slash) and a non-zero denominator displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole.
To add fractions, the denominators must be the same. If they are not, find a common denominator and convert each fraction to an equivalent fraction with that denominator.
To subtract fractions, the denominators must be the same. If they are not, find a common denominator and convert each fraction to an equivalent fraction with that denominator.
To multiply fractions, multiply the numerators together and multiply the denominators together.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
Simplifying (or reducing) fractions means making the fraction as simple as possible. A fraction is considered simplified if there are no common factors (other than 1) between the numerator and the denominator.
The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. For example, the GCD of 8 and 12 is 4.
A mixed number is a whole number and a proper fraction combined. For example, 2 1/3 is a mixed number. It represents 2 + 1/3.
To convert a mixed number to an improper fraction:
To convert an improper fraction to a mixed number:
To convert a decimal to a fraction, follow these steps:
To convert a fraction to a decimal, simply divide the numerator by the denominator.
Some fractions result in repeating decimals:
If you have a pizza cut into 8 slices and you eat 3 slices:
If you answered 15 out of 20 questions correctly on a test:
If you need to cut a board that is 3/4 feet long from a 6-foot board:
If a recipe calls for 2/3 cup of flour and you want to make half the recipe:
If you want to calculate 25% of $80:
A proper fraction has a numerator that is smaller than the denominator (e.g., 3/4). An improper fraction has a numerator that is equal to or larger than the denominator (e.g., 5/4 or 4/4).
To add fractions with different denominators, first find a common denominator (usually the least common multiple of the denominators), convert both fractions to equivalent fractions with that denominator, then add the numerators.
A mixed number combines a whole number and a proper fraction, such as 2 1/3. It represents the sum of the whole number and the fraction (2 + 1/3).
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, to simplify 8/12, divide both 8 and 12 by 4 to get 2/3.
The reciprocal of a fraction is created by swapping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3.
To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/4 = 0.75 × 100 = 75%.
Equivalent fractions are different fractions that represent the same value. For example, 1/2, 2/4, and 3/6 are all equivalent fractions.