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Fraction Reckoner

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below stand for the denominator.

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Mixed Numbers Calculator

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Simplify Fractions Computer

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Decimal to Fraction Calculator

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Fraction to Decimal Calculator

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Big Number Fraction Figurer

Employ this figurer if the numerators or denominators are very big 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 full number of parts that brand upwards said whole. For instance, in the fraction of

, the numerator is iii, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would plant the numerator of a fraction, while the total of 8 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

every bit shown in the paradigm to the correct. Note that the denominator of a fraction cannot be 0, as information technology would make the fraction undefined. Fractions can undergo many dissimilar operations, some of which are mentioned beneath.

Addition:

Dissimilar adding 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 past the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to exist a multiple of each individual denominator. The numerators likewise need to be multiplied by the advisable factors to preserve the value of the fraction as a whole. This is arguably the simplest manner to ensure that the fractions accept a mutual denominator. However, in most cases, the solutions to these equations will not appear in simplified class (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the trouble by the product of the denominators of all the other fractions (not including its ain respective denominator) in the problem.

An alternative 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 ane would an integer. Using the least mutual multiple tin exist more efficient and is more probable to result in a fraction in simplified form. In the example above, the denominators were four, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

Multiples of ii: ii, four, 6, 8 x, 12

Multiples of 4: iv, 8, 12

Multiples of 6: 6, 12

The start multiple they all share is 12, so this is the to the lowest degree mutual multiple. To complete 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, and then add the numerators.

Subtraction:

Fraction subtraction is essentially the aforementioned as fraction addition. A mutual denominator is required for the operation to occur. Refer to the addition department equally well as the equations below for description.

Multiplication:

Multiplying fractions is adequately straightforward. Unlike adding and subtracting, it is not necessary to compute a mutual denominator in order to multiply fractions. Only, 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 clarification.

Division:

The process for dividing fractions is like to that for multiplying fractions. In gild 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 merely

. 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:

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

for example, is more cumbersome than

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

Converting betwixt fractions and decimals:

Converting from decimals to fractions is straightforward. It does, nonetheless, crave the agreement that each decimal place to the right of the decimal betoken represents a power of 10; the starting time decimal place being 10¹, the second 10ⁱⁱ, the third 10³, and then on. But determine what ability of 10 the decimal extends to, use that power of ten 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 four is in the quaternary decimal place, which constitutes ten⁴, or x,000. This would make the fraction

, which simplifies to

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

Similarly, fractions with denominators that are powers of ten (or tin be converted to powers of 10) tin be translated to decimal grade using the same principles. Take the fraction

for example. To convert this fraction into a decimal, start convert information technology into the fraction of

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

can be converted to 0.five. If the fraction were instead

, the decimal would then be 0.05, and then on. Across this, converting fractions into decimals requires the performance of long sectionalization.

Common Technology Fraction to Decimal Conversions

In engineering, 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	16^thursday	8^th	4^th	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
3/64						0.046875	i.190625
4/64	two/32	1/sixteen				0.0625	1.5875
5/64						0.078125	i.984375
six/64	3/32					0.09375	two.38125
7/64						0.109375	two.778125
viii/64	4/32	2/sixteen	i/8			0.125	3.175
9/64						0.140625	three.571875
x/64	v/32					0.15625	3.96875
xi/64						0.171875	4.365625
12/64	6/32	3/16				0.1875	4.7625
13/64						0.203125	five.159375
14/64	7/32					0.21875	v.55625
fifteen/64						0.234375	5.953125
sixteen/64	eight/32	four/16	2/eight	ane/4		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
19/64						0.296875	seven.540625
20/64	ten/32	5/16				0.3125	7.9375
21/64						0.328125	eight.334375
22/64	11/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	6/sixteen	three/8			0.375	ix.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	ten.715625
28/64	xiv/32	vii/16				0.4375	11.1125
29/64						0.453125	eleven.509375
30/64	15/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	4/8	ii/4	1/two	0.five	12.seven
33/64						0.515625	13.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	thirteen.890625
36/64	xviii/32	ix/16				0.5625	14.2875
37/64						0.578125	14.684375
38/64	19/32					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	11/xvi				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	6/8	iii/4		0.75	19.05
49/64						0.765625	xix.446875
fifty/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
52/64	26/32	13/sixteen				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	14/16	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	xxx/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	eight/eight	four/4	two/two	one	25.4