Fraction Calculator
Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals.
Simple Fraction Calculator
Mixed Numbers Calculator
Simplify Fractions Calculator
Decimal to Fraction Calculator
Fraction to Decimal Calculator
Big Number Fraction Calculator
Use this calculator if the numerators or denominators are very big integers.
Understanding Fractions
In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of 3/8, the numerator is 3, and the denominator is 8.
Addition:
Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction.
Example: 3/4 + 1/6 = (3×6 + 1×4) / (4×6) = 22/24 = 11/12
Subtraction:
Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur.
Example: 3/4 - 1/6 = (3×6 - 1×4) / (4×6) = 14/24 = 7/12
Multiplication:
Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions.
Example: 3/4 × 1/6 = 3/24 = 1/8
Division:
The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator.
Example: 3/4 ÷ 1/6 = 3/4 × 6/1 = 18/4 = 9/2
Simplification:
It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms. 220/440 for example, is more cumbersome than 1/2.
Converting between fractions and decimals:
Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, and so on.
Related Calculators
Fraction Quick Facts
- •The numerator represents how many parts you have, the denominator represents how many equal parts the whole is divided into
- •A proper fraction has a numerator smaller than the denominator (e.g., 3/4)
- •An improper fraction has a numerator equal to or larger than the denominator (e.g., 5/4)
- •A mixed number combines a whole number with a proper fraction (e.g., 1 1/4)
Frequently Asked Questions
What's the difference between a fraction and a decimal?
Fractions and decimals are two different ways to represent numbers that are not whole. Fractions use a numerator and denominator (like 3/4), while decimals use a decimal point (like 0.75). Both represent the same value, just in different forms.
How do you add fractions with different denominators?
To add fractions with different denominators, you first need to find a common denominator (usually the least common multiple of the denominators). Then, convert each fraction to an equivalent fraction with that denominator before adding the numerators.
Why can't you divide by zero in a fraction?
Division by zero is undefined in mathematics. In a fraction, the denominator represents how many parts the whole is divided into. If you divide something into 0 parts, it doesn't make logical sense, which is why denominators cannot be zero.
What are some real-world applications of fractions?
Fractions are used in cooking (recipe measurements), construction (measurements), finance (interest rates), medicine (dosage calculations), and many other everyday situations where quantities are not whole numbers.
How do you convert a repeating decimal to a fraction?
To convert a repeating decimal like 0.333... to a fraction: Let x = 0.333..., then 10x = 3.333..., subtract the original: 10x - x = 3.333... - 0.333... → 9x = 3 → x = 3/9 = 1/3. This method works for any repeating decimal.