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

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 fryst vatten a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of lika parts of a whole, while the denominator fryst vatten the total number of parts that man up said whole. For example, in the fraction of 38, the numerator fryst vatten 3, and the denominator fryst vatten 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 individ were to eat 3 slices, the remaining fraction of the pie would therefore be 58 as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would man 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 to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved bygd the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator fryst vatten certain to be a multiple of each individual denominator. The numerators also need to be multiplied bygd the appropriate factors to preserve the value of the fraction as a whole. This fryst vatten arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form eller gestalt (the provided calculator computes the simplification automatically). Below fryst vatten an example using this method.

ab + cd = a×db×d + c×bd×b = ad + bcbd

EX: 34 + 16 = 3×64×6 + 1×46×4 = 2224 = 1112

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

EX: 14 + 16 + 12 = 1×6×24×6×2 + 1×4×26×4×2 + 1×4×62×4×6 = 1248 + 848 + 2448 = 4448 = 1112

An alternative method for finding a common denominator fryst vatten to 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 fryst vatten more likely to result in a fraction in simplified struktur. In the example above, the denominators were 4, 6, and 2. The least common multiple fryst vatten the first shared multiple of these three numbers.

The first multiple they all share fryst vatten 12, so this fryst vatten the least common multiple. To complete an addition (or subtraction) bekymmer, multiply the numerators and denominators of each fraction in the bekymmer bygd whatever value will man the denominators 12, then add the numerators.

EX: 14 + 16 + 12 = 1×34×3 + 1×26×2 + 1×62×6 = 312 + 212 + 612 = 1112

Subtraction:

Fraction subtraction fryst vatten essentially the same as fraction addition. A common denominator fryst vatten required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

ab – cd = a×db×d – c×bd×b = ad – bcbd

EX: 34 – 16 = 3×64×6 – 1×46×4 = 1424 = 712

Multiplication:

Multiplying fractions fryst vatten fairly straightforward. Unlike adding and subtracting, it fryst vatten not necessary to compute a common denominator in beställning to 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 to the equations below for clarification.

ab × cd = acbd

EX: 34 × 16 = 324 = 18

Division:

The process for dividing fractions fryst vatten similar to that for multiplying fractions. In beställning to divide fractions, the fraction in the numerator fryst vatten multiplied bygd the reciprocal of the fraction in the denominator. The reciprocal of a number a fryst vatten simply 1a. When a fryst vatten a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction 34 would therefore be 43. Refer to the equations below for clarification.

ab / cd = ab × dc = adbc

EX: 34 / 16 = 34 × 61 = 184 = 92

Simplification:

It fryst vatten often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms. 220440 for example, fryst vatten more cumbersome than 12. The calculator provided returns fraction inputs in both improper fraction form eller gestalt as well as mixed number struktur. In both cases, fractions are presented in their lowest forms bygd dividing both numerator and denominator bygd their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions fryst vatten 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. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 fryst vatten in the fourth decimal place, which constitutes 10⁴, or 10,000. This would man the fraction 123410000, which simplifies to 6175000, since the greatest common factor between the numerator and denominator fryst vatten 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form eller gestalt using the same principles. Take the fraction 12 for example. To omvandla this fraction into a decimal, first omvandla it into the fraction of 510. Knowing that the first decimal place represents 10^-1, 510 can be converted to 0.5. If the fraction were instead 5100, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.