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Fraction Calculator

Below are multiple fraction calculators capable of improver, subtraction, multiplication, partition, simplification, and conversion betwixt fractions and decimals. Fields above the solid black line represent the numerator, while fields beneath represent the denominator.

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Mixed Numbers Calculator

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Simplify Fractions Reckoner

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Decimal to Fraction Reckoner

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Fraction to Decimal Estimator

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Large Number Fraction Calculator

Use this estimator 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. Information technology 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 8 slices. 1 of those viii slices would found the numerator of a fraction, while the total of eight slices that comprises the whole pie would exist the denominator. If a person were to swallow 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 exist 0, as it would make the fraction undefined. Fractions tin undergo many different operations, some of which are mentioned beneath.

Add-on:

Unlike calculation and subtracting integers such as 2 and 8, fractions crave 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 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 demand to exist multiplied by the advisable 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. However, in most cases, the solutions to these equations will not announced in simplified form (the provided reckoner computes the simplification automatically). Beneath is an case using this method.

This process can be used for any number of fractions. Just 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 respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the least mutual multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the to the lowest degree common multiple can be more than efficient and is more likely to consequence in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The to the lowest degree common multiple is the outset shared multiple of these three numbers.

Multiples of 2: 2, 4, 6, 8 10, 12

Multiples of 4: four, 8, 12

Multiples of 6: 6, 12

The first multiple they all share is 12, and so 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 by any value will make the denominators 12, then add the numerators.

Subtraction:

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

Multiplication:

Multiplying fractions is fairly straightforward. Unlike calculation and subtracting, information technology is non necessary to compute a common denominator in lodge to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the consequence forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Segmentation:

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 only

. 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 oft easier to piece of work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for case, is more cumbersome than

. The computer provided returns fraction inputs in both improper fraction form besides equally mixed number form. In both cases, fractions are presented in their everyman forms by dividing both numerator and denominator by 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 identify to the right of the decimal betoken represents a power of x; the kickoff decimal identify being 10ⁱ, the 2d ten^two, the third 10^three, and so on. Simply decide what power of 10 the decimal extends to, use that power of ten as the denominator, enter each number to the right of the decimal bespeak every bit the numerator, and simplify. For instance, looking at the number 0.1234, the number 4 is in the 4th decimal place, which constitutes 10⁴, or 10,000. This would make the fraction

, which simplifies to

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

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) tin exist translated to decimal form using the same principles. Accept the fraction

for case. To convert this fraction into a decimal, get-go convert it into the fraction of

. Knowing that the first decimal identify represents 10^-1,

can be converted to 0.5. If the fraction were instead

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

Mutual Engineering Fraction to Decimal Conversions

In technology, fractions are widely used to depict the size of components such every bit pipes and bolts. The most common fractional and decimal equivalents are listed below.

64^th	32^nd	sixteen^th	8^th	4^th	two^nd	Decimal	Decimal (inch to mm)
ane/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	ane.5875
5/64						0.078125	1.984375
six/64	3/32					0.09375	two.38125
7/64						0.109375	2.778125
8/64	4/32	two/sixteen	1/8			0.125	iii.175
nine/64						0.140625	three.571875
10/64	5/32					0.15625	3.96875
11/64						0.171875	iv.365625
12/64	half dozen/32	3/16				0.1875	4.7625
13/64						0.203125	v.159375
14/64	seven/32					0.21875	five.55625
xv/64						0.234375	5.953125
16/64	8/32	4/16	2/8	1/four		0.25	six.35
17/64						0.265625	6.746875
eighteen/64	9/32					0.28125	7.14375
xix/64						0.296875	7.540625
twenty/64	10/32	5/16				0.3125	vii.9375
21/64						0.328125	eight.334375
22/64	11/32					0.34375	eight.73125
23/64						0.359375	9.128125
24/64	12/32	vi/16	3/8			0.375	9.525
25/64						0.390625	nine.921875
26/64	13/32					0.40625	x.31875
27/64						0.421875	ten.715625
28/64	fourteen/32	7/16				0.4375	11.1125
29/64						0.453125	xi.509375
30/64	xv/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	sixteen/32	8/sixteen	4/8	2/4	1/ii	0.five	12.7
33/64						0.515625	13.096875
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	19/32					0.59375	xv.08125
39/64						0.609375	15.478125
twoscore/64	20/32	10/xvi	v/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	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	six/8	iii/4		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	thirteen/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	fourteen/xvi	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	thirty/32	15/xvi				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	8/8	4/four	2/2	1	25.4

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Source: https://www.calculator.net/fraction-calculator.html

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