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## Fraction Calculator

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

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## Large 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 make up said whole. For example, in the fraction of

, the numerator is 3, and the denominator is eight. A more illustrative case could involve a pie with eight slices. i of those 8 slices would constitute the numerator of a fraction, while the full of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be

equally shown in the image to the right. Annotation 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.

Unlike adding and subtracting integers such as 2 and eight, fractions require a common denominator to undergo these operations. One method for finding a mutual 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 sure to be a multiple of each individual denominator. The numerators likewise need to be multiplied by the appropriate factors to preserve the value of the fraction equally a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in near cases, the solutions to these equations volition not appear in simplified form (the provided reckoner computes the simplification automatically). Below is an case using this method.

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This process tin can exist used for whatever number of fractions. Merely multiply the numerators and denominators of each fraction in the problem by the production of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An culling method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add together or subtract the numerators as one would an integer. Using the least common multiple tin can be more efficient and is more likely to effect in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the get-go shared multiple of these 3 numbers.

 Multiples of 2: 2, iv, six, 8 10, 12 Multiples of iv: iv, viii, 12 Multiples of 6: six, 12

The first multiple they all share is 12, then this is the to the lowest degree common multiple. To complete an addition (or subtraction) trouble, multiply the numerators and denominators of each fraction in the trouble past whatever value will brand the denominators 12, then add the numerators.

### Subtraction:

Fraction subtraction is substantially the aforementioned as fraction addition. A common denominator is required for the operation to occur. Refer to the addition department equally well every bit the equations beneath for clarification.

### Multiplication:

Multiplying fractions is adequately straightforward. Unlike adding and subtracting, information technology is not necessary to compute a mutual denominator in order to multiply fractions. Only, the numerators and denominators of each fraction are multiplied, and the effect forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for description.

### Division:

The process for dividing fractions is similar to that for multiplying fractions. In guild to split up 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

would therefore be

. Refer to the equations below for clarification.

### Simplification:

It is oftentimes easier to work with simplified fractions. As such, fraction solutions are ordinarily expressed in their simplified forms.

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form also every bit mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common gene.

### Converting betwixt 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 signal represents a power of 10; the beginning decimal place being 101, the 2nd ten2, the third 10three, and so on. Simply determine what power of 10 the decimal extends to, employ that power of 10 equally the denominator, enter each number to the correct of the decimal point as the numerator, and simplify. For case, looking at the number 0.1234, the number iv is in the fourth decimal place, which constitutes 104, or x,000. This would brand the fraction

, which simplifies to

, 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 to powers of 10) can be translated to decimal class using the same principles. Take the fraction

for case. To convert this fraction into a decimal, outset convert information technology into the fraction of

. Knowing that the first decimal place represents ten-i,

can be converted to 0.5. If the fraction were instead

, the decimal would and so exist 0.05, and so on. Beyond this, converting fractions into decimals requires the functioning of long sectionalization.

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### Common Engineering Fraction to Decimal Conversions

In engineering, fractions are widely used to depict the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed beneath.

 64th 32nd 16th viiithursday 4thursday 2nd Decimal Decimal(inch to mm) 1/64 0.015625 0.396875 2/64 i/32 0.03125 0.79375 3/64 0.046875 1.190625 4/64 2/32 1/16 0.0625 1.5875 5/64 0.078125 1.984375 half-dozen/64 3/32 0.09375 2.38125 7/64 0.109375 two.778125 viii/64 4/32 2/16 i/8 0.125 3.175 nine/64 0.140625 3.571875 10/64 5/32 0.15625 3.96875 11/64 0.171875 iv.365625 12/64 vi/32 3/16 0.1875 4.7625 13/64 0.203125 5.159375 14/64 vii/32 0.21875 v.55625 15/64 0.234375 v.953125 16/64 viii/32 4/16 2/8 1/iv 0.25 vi.35 17/64 0.265625 6.746875 18/64 9/32 0.28125 vii.14375 19/64 0.296875 7.540625 20/64 10/32 5/xvi 0.3125 7.9375 21/64 0.328125 8.334375 22/64 11/32 0.34375 8.73125 23/64 0.359375 9.128125 24/64 12/32 half dozen/xvi 3/eight 0.375 9.525 25/64 0.390625 9.921875 26/64 13/32 0.40625 10.31875 27/64 0.421875 10.715625 28/64 14/32 vii/xvi 0.4375 xi.1125 29/64 0.453125 xi.509375 30/64 fifteen/32 0.46875 11.90625 31/64 0.484375 12.303125 32/64 16/32 8/16 iv/8 2/4 1/two 0.5 12.7 33/64 0.515625 13.096875 34/64 17/32 0.53125 13.49375 35/64 0.546875 13.890625 36/64 18/32 9/16 0.5625 14.2875 37/64 0.578125 xiv.684375 38/64 19/32 0.59375 15.08125 39/64 0.609375 15.478125 40/64 20/32 10/16 5/8 0.625 15.875 41/64 0.640625 16.271875 42/64 21/32 0.65625 xvi.66875 43/64 0.671875 17.065625 44/64 22/32 xi/16 0.6875 17.4625 45/64 0.703125 17.859375 46/64 23/32 0.71875 18.25625 47/64 0.734375 18.653125 48/64 24/32 12/sixteen 6/viii iii/4 0.75 19.05 49/64 0.765625 nineteen.446875 50/64 25/32 0.78125 19.84375 51/64 0.796875 twenty.240625 52/64 26/32 13/16 0.8125 20.6375 53/64 0.828125 21.034375 54/64 27/32 0.84375 21.43125 55/64 0.859375 21.828125 56/64 28/32 xiv/16 7/eight 0.875 22.225 57/64 0.890625 22.621875 58/64 29/32 0.90625 23.01875 59/64 0.921875 23.415625 60/64 thirty/32 15/16 0.9375 23.8125 61/64 0.953125 24.209375 62/64 31/32 0.96875 24.60625 63/64 0.984375 25.003125 64/64 32/32 16/sixteen viii/8 4/4 two/2 1 25.4

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