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Fraction Calculator

Below are multiple fraction calculators capable of add-on, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields in a higher place the solid blackness line stand for the numerator, while fields below represent the denominator.

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Mixed Numbers Reckoner

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Simplify Fractions Estimator

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Decimal to Fraction Estimator

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Fraction to Decimal Figurer

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Big Number Fraction Calculator

Use 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 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 8. A more illustrative example could involve a pie with viii slices. i of those 8 slices would constitute the numerator of a fraction, while the total of eight slices that comprises the whole pie would be the denominator. If a person were to consume iii slices, the remaining fraction of the pie would therefore be

as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as information technology would make the fraction undefined. Fractions tin can undergo many dissimilar operations, some of which are mentioned below.

Improver:

Unlike adding and subtracting integers such equally 2 and viii, fractions require a common denominator to undergo these operations. Ane 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 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 have a common denominator. Even so, in near cases, the solutions to these equations will non appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Simply 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 culling method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, and so add together or subtract the numerators as one would an integer. Using the least common multiple can exist more efficient and is more probable to consequence in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the starting time shared multiple of these three numbers.

Multiples of 2: 2, 4, vi, 8 10, 12

Multiples of 4: 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) trouble, multiply the numerators and denominators of each fraction in the trouble by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is substantially the same as fraction add-on. A common denominator is required for the operation to occur. Refer to the addition department as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, information technology is not necessary to compute a mutual denominator in social club to multiply fractions. Merely, the numerators and denominators of each fraction are multiplied, and the event forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Division:

The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is just

. 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:

Information technology is oftentimes easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for case, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form equally well 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 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 ability of x; the starting time decimal place beingness 10¹, the second 10^two, the tertiary 10³, and so on. But determine what power of 10 the decimal extends to, employ that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For instance, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes ten⁴, or 10,000. This would make the fraction

, which simplifies to

, since the greatest common gene 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 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 identify represents 10^-1,

tin be converted to 0.5. If the fraction were instead

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

Common Engineering science Fraction to Decimal Conversions

In technology, 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	sixteen^th	8^th	iv^th	2^nd	Decimal	Decimal (inch to mm)
ane/64						0.015625	0.396875
ii/64	1/32					0.03125	0.79375
three/64						0.046875	ane.190625
4/64	2/32	i/16				0.0625	one.5875
five/64						0.078125	1.984375
6/64	iii/32					0.09375	two.38125
7/64						0.109375	2.778125
8/64	four/32	2/16	i/viii			0.125	3.175
nine/64						0.140625	iii.571875
x/64	v/32					0.15625	3.96875
11/64						0.171875	4.365625
12/64	half dozen/32	iii/16				0.1875	4.7625
13/64						0.203125	v.159375
xiv/64	7/32					0.21875	5.55625
fifteen/64						0.234375	5.953125
xvi/64	8/32	4/sixteen	2/viii	1/4		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
xix/64						0.296875	vii.540625
20/64	ten/32	5/sixteen				0.3125	seven.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/16	3/8			0.375	ix.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	x.31875
27/64						0.421875	x.715625
28/64	fourteen/32	seven/sixteen				0.4375	eleven.1125
29/64						0.453125	xi.509375
xxx/64	xv/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	xvi/32	eight/16	four/8	two/4	1/2	0.five	12.7
33/64						0.515625	thirteen.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	18/32	ix/16				0.5625	14.2875
37/64						0.578125	14.684375
38/64	xix/32					0.59375	fifteen.08125
39/64						0.609375	xv.478125
xl/64	20/32	10/16	5/8			0.625	15.875
41/64						0.640625	16.271875
42/64	21/32					0.65625	16.66875
43/64						0.671875	17.065625
44/64	22/32	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	12/16	6/8	3/iv		0.75	19.05
49/64						0.765625	19.446875
fifty/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
52/64	26/32	13/xvi				0.8125	xx.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	fourteen/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
sixty/64	30/32	15/sixteen				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/xvi	8/eight	4/iv	2/2	1	25.4