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Fraction Computer
Below are multiple fraction calculators capable of improver, subtraction, multiplication, division, simplification, and conversion betwixt fractions and decimals. Fields above the solid blackness 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
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Fraction to Decimal Calculator
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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 role 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 8. A more illustrative case could involve a pie with eight slices. one of those 8 slices would establish the numerator of a fraction, while the total of 8 slices that comprises the whole pie would exist the denominator. If a person were to eat iii slices, the remaining fraction of the pie would therefore be
as shown in the image to the correct. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions tin can undergo many unlike operations, some of which are mentioned below.
Addition:
Unlike calculation and subtracting integers such every bit 2 and eight, fractions require a common denominator to undergo these operations. I 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 to be a multiple of each individual denominator. The numerators besides need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest manner to ensure that the fractions have a common denominator. Still, in most cases, the solutions to these equations will not announced in simplified class (the provided calculator computes the simplification automatically). Below is an instance using this method.
This process can be used for whatsoever number of fractions. Just 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 trouble.
An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, so add together or subtract the numerators as one would an integer. Using the to the lowest degree mutual multiple can exist more than efficient and is more likely to result in a fraction in simplified class. In the instance above, the denominators were 4, six, and 2. The least common multiple is the first shared multiple of these three numbers.
Multiples of ii: 2, 4, vi, 8 10, 12 
Multiples of 4: 4, eight, 12 
Multiples of six: 6, 12 
The starting time multiple they all share is 12, and so 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 brand the denominators 12, so add the numerators.
Subtraction:
Fraction subtraction is essentially the same as fraction addition. A mutual denominator is required for the operation to occur. Refer to the improver section also as the equations beneath for description.
Multiplication:
Multiplying fractions is fairly straightforward. Unlike calculation and subtracting, it is not necessary to compute a common denominator in order 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 beneath for description.
Segmentation:
The process for dividing fractions is similar to that for multiplying fractions. In order to separate 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 substantially 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 often easier to piece of work with simplified fractions. As such, fraction solutions are usually expressed in their simplified forms.
for case, is more cumbersome than
. The calculator provided returns fraction inputs in both improper fraction form also as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator past their greatest mutual factor.
Converting between fractions and decimals:
Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the correct of the decimal point represents a power of 10; the getgo decimal place being x^{1}, the second 10^{ii}, the third 10^{three}, and so on. Simply decide what power of ten the decimal extends to, use that power of 10 every bit 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 4 is in the fourth decimal place, which constitutes 10^{4}, or 10,000. This would make the fraction
, which simplifies to
, since the greatest common gene between the numerator and denominator is ii.
Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) tin can be translated to decimal grade using the same principles. Take the fraction
for instance. To convert this fraction into a decimal, beginning convert it into the fraction of
. Knowing that the commencement decimal place represents 10^{1},
can be converted to 0.5. If the fraction were instead
, the decimal would then exist 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.
Common Technology Fraction to Decimal Conversions
In engineering, fractions are widely used to draw the size of components such every bit pipes and bolts. The almost common partial and decimal equivalents are listed below.
64^{th}  32^{nd}  16^{th}  8^{th}  iv^{th}  ii^{nd}  Decimal  Decimal (inch to mm) 
1/64  0.015625  0.396875  
2/64  1/32  0.03125  0.79375  
3/64  0.046875  ane.190625  
4/64  2/32  ane/16  0.0625  1.5875  
5/64  0.078125  i.984375  
6/64  3/32  0.09375  2.38125  
seven/64  0.109375  2.778125  
8/64  4/32  2/16  1/viii  0.125  3.175  
nine/64  0.140625  three.571875  
10/64  5/32  0.15625  3.96875  
xi/64  0.171875  4.365625  
12/64  6/32  3/sixteen  0.1875  iv.7625  
13/64  0.203125  v.159375  
fourteen/64  7/32  0.21875  5.55625  
15/64  0.234375  v.953125  
16/64  8/32  four/xvi  ii/viii  1/4  0.25  6.35  
17/64  0.265625  6.746875  
18/64  nine/32  0.28125  7.14375  
nineteen/64  0.296875  7.540625  
twenty/64  10/32  five/16  0.3125  vii.9375  
21/64  0.328125  8.334375  
22/64  11/32  0.34375  viii.73125  
23/64  0.359375  9.128125  
24/64  12/32  6/16  iii/eight  0.375  9.525  
25/64  0.390625  9.921875  
26/64  xiii/32  0.40625  10.31875  
27/64  0.421875  10.715625  
28/64  14/32  7/sixteen  0.4375  xi.1125  
29/64  0.453125  eleven.509375  
30/64  15/32  0.46875  11.90625  
31/64  0.484375  12.303125  
32/64  16/32  8/16  4/8  ii/4  1/2  0.five  12.vii 
33/64  0.515625  thirteen.096875  
34/64  17/32  0.53125  13.49375  
35/64  0.546875  13.890625  
36/64  18/32  9/xvi  0.5625  xiv.2875  
37/64  0.578125  14.684375  
38/64  nineteen/32  0.59375  15.08125  
39/64  0.609375  15.478125  
40/64  20/32  ten/16  5/8  0.625  15.875  
41/64  0.640625  sixteen.271875  
42/64  21/32  0.65625  sixteen.66875  
43/64  0.671875  17.065625  
44/64  22/32  11/16  0.6875  17.4625  
45/64  0.703125  17.859375  
46/64  23/32  0.71875  eighteen.25625  
47/64  0.734375  18.653125  
48/64  24/32  12/16  vi/8  iii/4  0.75  19.05  
49/64  0.765625  19.446875  
50/64  25/32  0.78125  nineteen.84375  
51/64  0.796875  20.240625  
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  14/sixteen  vii/viii  0.875  22.225  
57/64  0.890625  22.621875  
58/64  29/32  0.90625  23.01875  
59/64  0.921875  23.415625  
threescore/64  30/32  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  16/16  viii/viii  4/four  two/2  1  25.iv 
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Source: https://www.calculator.net/fractioncalculator.html