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Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid Đen line represent the numerator, while fields below represent the denominator.

Mixed Numbers Calculator

Simplify Fractions Calculator

Decimal đồ sộ Fraction Calculator

Fraction đồ sộ Decimal Calculator

Big Number Fraction Calculator

Use this calculator if the numerators or denominators are very big integers.

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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 trang điểm said whole. For example, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were đồ sộ eat 3 slices, the remaining fraction of the pie would therefore be

as shown in the image đồ sộ the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator đồ sộ 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. Multiplying all of the denominators ensures that the new denominator is certain đồ sộ be a multiple of each individual denominator. The numerators also need đồ sộ be multiplied by the appropriate factors đồ sộ preserve the value of the fraction as a whole. This is arguably the simplest way đồ sộ ensure that the fractions have a common denominator. However, in most cases, the solutions đồ sộ these equations will not appear in simplified size (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An alternative method for finding a common denominator is đồ sộ determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely đồ sộ result in a fraction in simplified size. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

The first multiple they all share is 12, sánh this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation đồ sộ occur. Refer đồ sộ the addition section as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary đồ sộ compute a common denominator in order đồ sộ multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer đồ sộ the equations below for clarification.

Division:

The process for dividing fractions is similar đồ sộ that for multiplying fractions. In order đồ sộ divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply

. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction

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would therefore be

. Refer đồ sộ the equations below for clarification.

Simplification:

It is often easier đồ sộ work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome phàn nàn

. The calculator provided returns fraction inputs in both improper fraction size as well as mixed number size. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals đồ sộ fractions is straightforward. It does, however, require the understanding that each decimal place đồ sộ the right of the decimal point represents a power of 10; the first decimal place being 10¹, the second 10², the third 10³, and sánh on. Simply determine what power of 10 the decimal extends đồ sộ, use that power of 10 as the denominator, enter each number đồ sộ the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10⁴, or 10,000. This would make the fraction

, which simplifies đồ sộ

, since the greatest common factor between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted đồ sộ powers of 10) can be translated đồ sộ decimal size using the same principles. Take the fraction

for example. To convert this fraction into a decimal, first convert it into the fraction of

. Knowing that the first decimal place represents 10^-1,

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can be converted đồ sộ 0.5. If the fraction were instead

, the decimal would then be 0.05, and sánh on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction đồ sộ Decimal Conversions

In engineering, fractions are widely used đồ sộ describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.