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Fraction Calculator

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

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Big Number Fraction Estimator

Use this figurer 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. 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 three, and the denominator is eight. A more illustrative example could involve a pie with eight slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of viii slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore exist

equally shown in the image to the correct. Notation that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many dissimilar operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such equally ii and 8, fractions require a common denominator to undergo these operations. I 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 private 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 mode to ensure that the fractions take a common denominator. Still, in about cases, the solutions to these equations will not announced in simplified form (the provided computer computes the simplification automatically). Below is an example using this method.

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

An culling method for finding a mutual denominator is to make up one's mind the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more than efficient and is more likely to result in a fraction in simplified form. In the instance higher up, the denominators were 4, 6, and 2. The least common multiple is the get-go shared multiple of these iii numbers.

Multiples of 2: 2, four, 6, viii 10, 12

Multiples of 4: 4, 8, 12

Multiples of 6: 6, 12

The outset multiple they all share is 12, so this is the least mutual multiple. To consummate an add-on (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, so add together the numerators.

Subtraction:

Fraction subtraction is essentially the aforementioned as fraction addition. A mutual denominator is required for the performance to occur. Refer to the addition section as well every bit the equations beneath for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Dissimilar adding and subtracting, information technology is not necessary to compute a common denominator in guild to multiply fractions. Merely, 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.

Division:

The process for dividing fractions is similar to that for multiplying fractions. In social club 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 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 clarification.

Simplification:

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

for example, is more than cumbersome than

. The calculator provided returns fraction inputs in both improper fraction course too every bit mixed number form. In both cases, fractions are presented in their everyman forms past dividing both numerator and denominator by their greatest common factor.

Converting betwixt fractions and decimals:

Converting from decimals to fractions is straightforward. Information technology does, however, require the agreement that each decimal place to the correct of the decimal bespeak represents a ability of 10; the first decimal place being 10¹, the 2d x^two, the third 10³, and so on. Simply determine what power of ten the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal indicate equally the numerator, and simplify. For example, looking at the number 0.1234, the number four is in the fourth decimal identify, which constitutes 10^four, or x,000. This would brand 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 tin can exist converted to powers of 10) tin can be translated to decimal class using the same principles. Take the fraction

for example. To convert this fraction into a decimal, kickoff convert it into the fraction of

. Knowing that the start decimal identify represents ten^-1,

can 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.

Mutual Engineering Fraction to Decimal Conversions

In engineering science, 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	viii^th	4^th	2^nd	Decimal	Decimal (inch to mm)
i/64						0.015625	0.396875
2/64	one/32					0.03125	0.79375
3/64						0.046875	ane.190625
4/64	2/32	1/16				0.0625	1.5875
v/64						0.078125	1.984375
half dozen/64	3/32					0.09375	ii.38125
7/64						0.109375	two.778125
8/64	iv/32	2/16	i/8			0.125	3.175
ix/64						0.140625	3.571875
10/64	v/32					0.15625	three.96875
11/64						0.171875	4.365625
12/64	6/32	3/sixteen				0.1875	four.7625
thirteen/64						0.203125	five.159375
14/64	7/32					0.21875	5.55625
15/64						0.234375	5.953125
sixteen/64	8/32	4/sixteen	ii/eight	i/4		0.25	half-dozen.35
17/64						0.265625	6.746875
eighteen/64	9/32					0.28125	seven.14375
19/64						0.296875	seven.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	6/16	iii/8			0.375	ix.525
25/64						0.390625	ix.921875
26/64	thirteen/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	14/32	7/16				0.4375	11.1125
29/64						0.453125	11.509375
thirty/64	xv/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	four/8	2/iv	1/2	0.5	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	xviii/32	nine/sixteen				0.5625	14.2875
37/64						0.578125	fourteen.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	15.478125
xl/64	20/32	10/16	5/eight			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/xvi				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/viii	three/iv		0.75	19.05
49/64						0.765625	nineteen.446875
fifty/64	25/32					0.78125	19.84375
51/64						0.796875	xx.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	14/16	7/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
60/64	30/32	xv/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	16/16	8/eight	4/4	ii/ii	1	25.four