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Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, segmentation, simplification, and conversion betwixt fractions and decimals. Fields to a higher place the solid black line represent the numerator, while fields beneath represent the denominator.

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Mixed Numbers Computer

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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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Large Number Fraction Calculator

Apply this calculator if the numerators or denominators are very large 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 brand upwardly said whole. For example, in the fraction of

, the numerator is 3, and the denominator is 8. A more than illustrative example could involve a pie with 8 slices. 1 of those eight slices would constitute 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 swallow three slices, the remaining fraction of the pie would therefore exist

as shown in the image to the right. Notation that the denominator of a fraction cannot exist 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned beneath.

Addition:

Different adding and subtracting integers such as 2 and 8, fractions require 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 production 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 also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions accept a common denominator. Still, in virtually cases, the solutions to these equations will not appear in simplified class (the provided calculator computes the simplification automatically). Below is an instance using this method.

This procedure tin can exist used for any number of fractions. Only multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its ain corresponding 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 decrease the numerators as one would an integer. Using the least common multiple can exist more efficient and is more than likely to outcome in a fraction in simplified grade. In the case above, the denominators were 4, 6, and two. The least mutual multiple is the showtime shared multiple of these three numbers.

Multiples of two: two, iv, vi, 8 10, 12

Multiples of 4: four, viii, 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 by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same equally fraction addition. A common denominator is required for the operation to occur. Refer to the addition section every bit well equally the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is non 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 below for description.

Partition:

The process for dividing fractions is similar to that for multiplying fractions. In order 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 exist

. Refer to the equations below for description.

Simplification:

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

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form likewise as mixed number form. In both cases, fractions are presented in their everyman forms past dividing both numerator and denominator past their greatest common 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 right of the decimal point represents a power of 10; the first decimal place being 10¹, the second 10^two, the 3rd 10³, and so on. Simply determine what power of 10 the decimal extends to, apply that power of x every bit the denominator, enter each number to the right of the decimal indicate as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the quaternary decimal identify, which constitutes 10^iv, or 10,000. This would brand the fraction

, which simplifies to

, since the greatest common factor between the numerator and denominator is ii.

Similarly, fractions with denominators that are powers of ten (or can be converted to powers of ten) can exist translated to decimal form using the same principles. Take the fraction

for example. To catechumen this fraction into a decimal, first catechumen it into the fraction of

. Knowing that the first decimal place represents 10^-ane,

can be converted to 0.5. If the fraction were instead

, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long partition.

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 below.

64^th	32^nd	16^th	eight^thursday	4^th	two^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
iii/64						0.046875	1.190625
iv/64	ii/32	i/16				0.0625	1.5875
5/64						0.078125	ane.984375
6/64	3/32					0.09375	2.38125
7/64						0.109375	2.778125
viii/64	four/32	2/sixteen	1/8			0.125	iii.175
nine/64						0.140625	three.571875
ten/64	v/32					0.15625	three.96875
xi/64						0.171875	4.365625
12/64	half dozen/32	3/sixteen				0.1875	4.7625
13/64						0.203125	5.159375
14/64	7/32					0.21875	5.55625
fifteen/64						0.234375	5.953125
sixteen/64	8/32	4/xvi	2/8	1/4		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	vii.14375
nineteen/64						0.296875	7.540625
20/64	10/32	5/sixteen				0.3125	7.9375
21/64						0.328125	8.334375
22/64	xi/32					0.34375	8.73125
23/64						0.359375	ix.128125
24/64	12/32	six/16	3/8			0.375	9.525
25/64						0.390625	9.921875
26/64	thirteen/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	fourteen/32	7/xvi				0.4375	11.1125
29/64						0.453125	11.509375
30/64	15/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	sixteen/32	8/16	four/8	2/4	ane/2	0.five	12.7
33/64						0.515625	thirteen.096875
34/64	17/32					0.53125	thirteen.49375
35/64						0.546875	thirteen.890625
36/64	xviii/32	9/16				0.5625	14.2875
37/64						0.578125	14.684375
38/64	xix/32					0.59375	xv.08125
39/64						0.609375	15.478125
40/64	20/32	10/16	five/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	11/sixteen				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	12/16	6/8	3/4		0.75	19.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	19.84375
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	xiv/xvi	seven/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	30/32	fifteen/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/8	4/4	2/2	1	25.4