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Fraction Computer

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

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Mixed Numbers Reckoner

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Simplify Fractions Computer

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Decimal to Fraction Reckoner

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Fraction to Decimal Reckoner

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Big Number Fraction Calculator

Use this reckoner if the numerators or denominators are very big integers.

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In mathematics, a fraction is a number that represents a function 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 full number of parts that brand up said whole. For example, in the fraction of

, the numerator is iii, and the denominator is eight. A more than illustrative example could involve a pie with 8 slices. 1 of those viii slices would constitute 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 be

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

Addition:

Unlike calculation and subtracting integers such as 2 and 8, fractions require a common 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 sure 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 equally a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. Nevertheless, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process tin can be 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 corresponding denominator) in the problem.

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

Multiples of 2: two, 4, half dozen, eight 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 problem by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the aforementioned every bit fraction addition. A common denominator is required for the operation to occur. Refer to the addition section too as the equations below for description.

Multiplication:

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

Division:

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 be

. Refer to the equations below for clarification.

Simplification:

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

for case, is more than cumbersome than

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

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. Information technology does, withal, require the understanding that each decimal place to the right of the decimal point represents a power of x; the outset decimal identify being 10^ane, the 2d 10², the third 10^three, and so on. Simply determine what power of 10 the decimal extends to, apply that power of ten as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the quaternary decimal place, which constitutes x⁴, or 10,000. This would brand the fraction

, which simplifies to

, since the greatest common factor between the numerator and denominator is 2.

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

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

. Knowing that the first decimal place represents ten^-1,

can be converted to 0.5. If the fraction were instead

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

Common Technology Fraction to Decimal Conversions

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

64^thursday	32^nd	sixteen^thursday	8^th	4^th	2^nd	Decimal	Decimal (inch to mm)
ane/64						0.015625	0.396875
2/64	one/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	two/32	1/sixteen				0.0625	1.5875
v/64						0.078125	1.984375
6/64	3/32					0.09375	two.38125
seven/64						0.109375	2.778125
eight/64	4/32	ii/16	one/8			0.125	3.175
9/64						0.140625	three.571875
10/64	5/32					0.15625	3.96875
11/64						0.171875	four.365625
12/64	6/32	3/16				0.1875	4.7625
13/64						0.203125	5.159375
xiv/64	seven/32					0.21875	5.55625
fifteen/64						0.234375	five.953125
16/64	viii/32	4/16	2/8	one/four		0.25	6.35
17/64						0.265625	6.746875
eighteen/64	ix/32					0.28125	7.14375
nineteen/64						0.296875	seven.540625
20/64	10/32	5/16				0.3125	seven.9375
21/64						0.328125	viii.334375
22/64	eleven/32					0.34375	8.73125
23/64						0.359375	nine.128125
24/64	12/32	vi/16	3/8			0.375	ix.525
25/64						0.390625	ix.921875
26/64	13/32					0.40625	ten.31875
27/64						0.421875	x.715625
28/64	14/32	7/16				0.4375	11.1125
29/64						0.453125	eleven.509375
thirty/64	15/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	4/8	ii/4	1/2	0.five	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	xiii.49375
35/64						0.546875	13.890625
36/64	18/32	9/xvi				0.5625	14.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	15.478125
twoscore/64	20/32	10/16	five/8			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	18.25625
47/64						0.734375	xviii.653125
48/64	24/32	12/sixteen	half dozen/8	3/4		0.75	19.05
49/64						0.765625	xix.446875
50/64	25/32					0.78125	nineteen.84375
51/64						0.796875	20.240625
52/64	26/32	xiii/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/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	thirty/32	15/16				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	8/eight	4/4	2/2	1	25.4