Fraction Reckoner
Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line correspond the numerator, while fields below stand for 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 Estimator
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 office 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 instance could involve a pie with 8 slices. 1 of those 8 slices would institute 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 swallow 3 slices, the remaining fraction of the pie would therefore exist
equally shown in the image to the right. Note that the denominator of a fraction cannot be 0, every bit it would brand the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.
Addition:
Unlike adding and subtracting integers such equally 2 and 8, fractions crave a mutual denominator to 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 to exist a multiple of each individual denominator. The numerators also need to be multiplied past the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions take a common denominator. However, in most cases, the solutions to these equations will not appear in simplified grade (the provided calculator computes the simplification automatically). Beneath is an example using this method.
This process can be used for any number of fractions. Merely multiply the numerators and denominators of each fraction in the problem past the product of the denominators of all the other fractions (not including its own corresponding denominator) in the problem.
An alternative method for finding a common denominator is to make up one’s mind the to the lowest degree common multiple (LCM) for the denominators, then add together or decrease the numerators as one would an integer. Using the least common multiple tin be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, vi, and two. The least common multiple is the starting time shared multiple of these three numbers.
Multiples of 2: 2, 4, 6, 8 10, 12 
Multiples of iv: 4, 8, 12 
Multiples of 6: 6, 12 
The first multiple they all share is 12, 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 past whatever value volition 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 to occur. Refer to the addition section equally well as the equations below for clarification.
Multiplication:
Multiplying fractions is fairly straightforward. Dissimilar adding and subtracting, information technology is non necessary to compute a common denominator in guild 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 clarification.
Division:
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 but
. 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 description.
Simplification:
It is often easier to piece of work with simplified fractions. As such, fraction solutions are normally expressed in their simplified forms.
for example, is more cumbersome than
. The calculator provided returns fraction inputs in both improper fraction form too every bit mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator past their greatest common gene.
Converting betwixt fractions and decimals:
Converting from decimals to fractions is straightforward. Information technology does, however, require the understanding that each decimal identify to the correct of the decimal point represents a power of 10; the kickoff decimal place being x^{1}, the 2d x^{2}, the third 10^{three}, and so on. Simply determine what ability of 10 the decimal extends to, employ that ability of 10 as the denominator, enter each number to the right of the decimal point equally the numerator, and simplify. For case, looking at the number 0.1234, the number 4 is in the 4th decimal place, which constitutes x^{four}, or 10,000. This would make the fraction
, which simplifies to
, since the greatest common factor betwixt the numerator and denominator is ii.
Similarly, fractions with denominators that are powers of 10 (or can exist converted to powers of ten) tin can be translated to decimal form using the same principles. Take the fraction
for example. To convert this fraction into a decimal, first convert information technology into the fraction of
. Knowing that the first decimal place represents 10^{one},
can be converted to 0.five. If the fraction were instead
, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the performance of long division.
Common Engineering Fraction to Decimal Conversions
In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.
64^{th}  32^{nd}  16^{thursday}  8^{thursday}  4^{th}  two^{nd}  Decimal  Decimal (inch to mm) 
1/64  0.015625  0.396875  
ii/64  one/32  0.03125  0.79375  
3/64  0.046875  1.190625  
4/64  2/32  ane/sixteen  0.0625  ane.5875  
five/64  0.078125  1.984375  
6/64  3/32  0.09375  2.38125  
seven/64  0.109375  2.778125  
8/64  4/32  2/16  one/eight  0.125  3.175  
nine/64  0.140625  3.571875  
10/64  v/32  0.15625  iii.96875  
11/64  0.171875  4.365625  
12/64  6/32  3/16  0.1875  4.7625  
xiii/64  0.203125  5.159375  
14/64  vii/32  0.21875  5.55625  
xv/64  0.234375  five.953125  
16/64  8/32  iv/16  ii/8  1/iv  0.25  6.35  
17/64  0.265625  6.746875  
18/64  9/32  0.28125  7.14375  
19/64  0.296875  7.540625  
20/64  ten/32  v/xvi  0.3125  7.9375  
21/64  0.328125  8.334375  
22/64  11/32  0.34375  8.73125  
23/64  0.359375  ix.128125  
24/64  12/32  vi/16  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/16  0.4375  11.1125  
29/64  0.453125  xi.509375  
thirty/64  15/32  0.46875  11.90625  
31/64  0.484375  12.303125  
32/64  16/32  8/sixteen  4/8  2/iv  1/2  0.5  12.7 
33/64  0.515625  13.096875  
34/64  17/32  0.53125  xiii.49375  
35/64  0.546875  13.890625  
36/64  eighteen/32  9/16  0.5625  fourteen.2875  
37/64  0.578125  xiv.684375  
38/64  19/32  0.59375  xv.08125  
39/64  0.609375  15.478125  
40/64  20/32  10/sixteen  5/eight  0.625  fifteen.875  
41/64  0.640625  16.271875  
42/64  21/32  0.65625  16.66875  
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  eighteen.653125  
48/64  24/32  12/sixteen  6/8  3/4  0.75  19.05  
49/64  0.765625  xix.446875  
l/64  25/32  0.78125  19.84375  
51/64  0.796875  20.240625  
52/64  26/32  xiii/xvi  0.8125  twenty.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  14/16  7/8  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  xxx/32  xv/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  xvi/xvi  viii/8  4/4  two/2  1  25.four 
1/3 Divided by 7 as a Fraction
Source: https://www.calculator.net/fractioncalculator.html
Originally posted 20220802 13:27:30.