Fraction Calculator

Below are several fraction calculators that can perform addition, subtraction, multiplication, division, simplification, and convert between fractions and decimals. The fields above the solid black line represent numerators, and the fields below the line represent denominators.

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.

In mathematics, a fraction is a way of expressing a portion of a whole. It is made up of two numbers: the numerator and the denominator. The numerator indicates how many parts are being considered, while the denominator shows how many equal parts the whole is divided into. For instance, in the fraction $\frac{3}{8}$83​, the numerator is 3 and the denominator is 8.

A helpful example is a pie cut into 8 equal slices. Each single slice represents 1 out of the 8 total slices, forming a fraction. If someone eats 3 slices, 5 slices remain, which can be written as $\frac{5}{8}$85​. It is important to note that a denominator cannot be 0, because a fraction with a denominator of 0 is undefined. Fractions can be manipulated in various ways, and several common operations are discussed below."

Addition:

Unlike adding or subtracting whole numbers such as 2 and 8, performing these operations with fractions requires establishing a common denominator. One straightforward way to create a common denominator is to multiply each fraction’s numerator and denominator by the product of all denominators involved. This guarantees that the resulting denominator will be a multiple of every original denominator. The numerators must also be multiplied by the corresponding factors to ensure the overall value of each fraction remains unchanged. Although this method is often the easiest way to generate a common denominator, the resulting fractions are typically not in simplest form (the provided calculator will simplify them automatically). An example using this approach is shown below.

This method works for any number of fractions. To apply it, multiply each fraction’s numerator and denominator by the product of the denominators of all the other fractions in the problem (excluding its own denominator).

Another way to find a common denominator is to use the least common multiple (LCM) of the denominators. Once the LCM is determined, the fractions can be added or subtracted just like whole numbers. Using the LCM is often more efficient and can lead to a fraction that is already in simplified form.

For example, consider the denominators 4, 6, and 2. The least common multiple is the smallest number that all three denominators divide evenly into.

• Multiples of 2: 2, 4, 6, 8, 10, 12
• Multiples of 4: 4, 8, 12
• Multiples of 6: 6, 12

The first common multiple of 2, 4, and 6 is 12, which becomes the least common denominator.

The smallest multiple that all the denominators share is 12, making it the least common multiple. To perform the addition (or subtraction), adjust each fraction so that its denominator becomes 12 by multiplying both its numerator and denominator by the necessary factor. Once the denominators are the same, simply add (or subtract) the numerators

Subtraction:

Subtracting fractions works in the same way as adding them. A common denominator is needed before performing the operation. See the addition section and the examples below for guidance.

Multiplication:

Multiplying fractions is quite simple. Unlike addition and subtraction, you do not need a common denominator. To multiply fractions, simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. The result should be simplified whenever possible. See the examples below for clarification.

Division:

Dividing fractions is similar to multiplying them. To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a number $a$a is $\frac{1}{a}$a1​. For a fraction, finding the reciprocal means swapping its numerator and denominator. For example, the reciprocal of $\frac{3}{4}$43​ is $\frac{4}{3}$34​. See the examples below for clarification.

Simplification:

Working with simplified fractions is usually easier, so solutions are typically expressed in their simplest form. For example, $\frac{220}{440}$440220​ is more cumbersome than $\frac{1}{2}$21​. The calculator provided shows fractions both as improper fractions and as mixed numbers. In either case, fractions are simplified by dividing the numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting decimals to fractions is relatively straightforward, but it requires understanding that each decimal place represents a power of 10: the first decimal place is $10^1$101, the second is $10^2$102, the third is $10^3$103, and so on. To convert a decimal to a fraction, identify the place value of the last digit, use the corresponding power of 10 as the denominator, place the digits to the right of the decimal point as the numerator, and simplify the fraction convert to percentage.

For example, consider the number 0.1234. The digit 4 is in the fourth decimal place, which corresponds to $10^4 = 10,000$104=10,000. This gives the fraction $\frac{1234}{10000}$100001234​, which can be simplified to $\frac{617}{5000}$5000617​ by dividing both numerator and denominator by their greatest common factor, 2.

Conversely, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be converted to decimals using the same principle. For instance, $\frac{1}{2}$21​ can be expressed as $\frac{5}{10}$105​, which equals 0.5, since the first decimal place represents $10^{-1}$10−1. Similarly, $\frac{5}{100}$1005​ converts to 0.05, and so on. For fractions that cannot be easily expressed with denominators as powers of 10, converting to decimals requires performing long division.

Frequently Asked Questions.

What is the definition of a fraction?

A fraction is a way to represent a part of a whole. It consists of two numbers: the numerator, which shows how many parts are being considered, and the denominator, which shows the total number of equal parts that make up the whole. For example, in $\frac{3}{4}$43​, 3 is the numerator and 4 is the denominator.

What are the 7 types of fractions?

Fractions can be categorized into seven common types:

1. Proper fractions – numerator < denominator (e.g., $\frac{3}{4}$43​)
2. Improper fractions – numerator ≥ denominator (e.g., $\frac{7}{4}$47​)
3. Mixed numbers – a whole number combined with a proper fraction (e.g., $1\frac{3}{4}$143​)
4. Like fractions – fractions with the same denominator (e.g., $\frac{2}{5}$52​ and $\frac{3}{5}$53​)
5. Unlike fractions – fractions with different denominators (e.g., $\frac{2}{5}$52​ and $\frac{3}{7}$73​)
6. Equivalent fractions – fractions that represent the same value (e.g., $\frac{1}{2}$21​ and $\frac{2}{4}$42​)
7. Decimal fractions – fractions expressed with denominators as powers of 10 (e.g., $0.75 = \frac{75}{100}$0.75=10075​)

What is 0.333333333333333 as a fraction?

The repeating decimal $0.\overline{3}$0.3 can be written as the fraction $\frac{1}{3}$31​.

How to solve for fractions?

Solving fractions depends on the operation:

• Addition/Subtraction – Find a common denominator, adjust the numerators accordingly, then add or subtract the numerators. Simplify the result.
• Multiplication – Multiply the numerators together and the denominators together, then simplify.
• Division – Multiply the first fraction by the reciprocal of the second fraction, then simplify.
• Conversion – Fractions can also be converted to decimals (by dividing numerator by denominator) or to percentages (by multiplying the decimal by 100).

What is a Fraction Calculator?

A Fraction Calculator is an online tool that solves fraction problems instantly. It can add, subtract, multiply, divide, simplify fractions, and convert them to decimals or percentages.