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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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Mixed Numbers Calculator
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Simplify Fractions Calculator
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Decimal to Fraction Calculator
Result
Adding steps:
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Fraction to Decimal Calculator
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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.
Addition:
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.
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 getgo 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 10^{1}, the 2nd ten^{2}, the third 10^{three}, 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 10^{4}, 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.
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.
64^{th}  32^{nd}  16^{th}  viii^{thursday}  4^{thursday}  2^{nd}  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  
halfdozen/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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