2 Divided By One Fifth

Fraction Calculator

Beneath 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 correspond the denominator.

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Mixed Numbers Calculator

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Simplify Fractions Calculator

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Decimal to Fraction Estimator

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Adding steps:

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Fraction to Decimal Calculator

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Big Number Fraction Calculator

Utilise this calculator 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 total number of parts that make up said whole. For instance, 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 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 be

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

Addition:

Unlike adding and subtracting integers such every bit 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 private denominator. The numerators likewise demand to be multiplied past the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest mode to ensure that the fractions have a common denominator. However, in virtually cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Beneath is an instance using this method.

This process tin be used for whatsoever 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 (non including its ain respective denominator) in the problem.

An alternative method for finding a mutual denominator is to determine the least mutual multiple (LCM) for the denominators, so add or decrease the numerators as one would an integer. Using the to the lowest degree common multiple tin can be more efficient and is more likely to effect in a fraction in simplified course. In the case above, the denominators were 4, 6, and ii. The least common multiple is the showtime shared multiple of these three numbers.

Multiples of two: 2, iv, 6, 8 10, 12

Multiples of 4: 4, eight, 12

Multiples of 6: 6, 12

The first multiple they all share is 12, and so this is the least common multiple. To complete an add-on (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will brand the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the aforementioned every bit fraction improver. A common denominator is required for the operation to occur. Refer to the addition section too equally the equations beneath for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike calculation and subtracting, it is non necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result 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 past 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 description.

Simplification:

It is often easier to work with simplified fractions. Every bit such, fraction solutions are usually expressed in their simplified forms.

for example, is more cumbersome than

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

Converting betwixt fractions and decimals:

Converting from decimals to fractions is straightforward. Information technology does, still, require the understanding that each decimal identify to the correct of the decimal point represents a power of x; the first decimal place beingness 10¹, the 2d 10², the third ten³, and then on. Simply determine what power of 10 the decimal extends to, utilise that power of 10 as the denominator, enter each number to the right of the decimal point equally the numerator, and simplify. For instance, looking at the number 0.1234, the number 4 is in the 4th decimal identify, which constitutes 10^iv, or 10,000. This would make 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 tin can be converted to powers of 10) tin be translated to decimal form using the same principles. Take the fraction

for case. To catechumen this fraction into a decimal, commencement convert it into the fraction of

. Knowing that the first decimal place represents 10^-i,

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

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

Common Technology Fraction to Decimal Conversions

In applied science, fractions are widely used to draw the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.

64^thursday	32^nd	16^th	8^thursday	four^th	2^nd	Decimal	Decimal (inch to mm)
i/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
3/64						0.046875	one.190625
4/64	2/32	1/16				0.0625	1.5875
5/64						0.078125	one.984375
6/64	three/32					0.09375	2.38125
7/64						0.109375	2.778125
8/64	4/32	2/16	1/8			0.125	3.175
9/64						0.140625	three.571875
10/64	5/32					0.15625	three.96875
11/64						0.171875	4.365625
12/64	6/32	3/16				0.1875	4.7625
13/64						0.203125	5.159375
14/64	7/32					0.21875	five.55625
xv/64						0.234375	5.953125
sixteen/64	8/32	4/sixteen	ii/8	i/4		0.25	6.35
17/64						0.265625	6.746875
18/64	nine/32					0.28125	7.14375
nineteen/64						0.296875	vii.540625
20/64	ten/32	five/16				0.3125	seven.9375
21/64						0.328125	8.334375
22/64	xi/32					0.34375	viii.73125
23/64						0.359375	ix.128125
24/64	12/32	6/16	3/8			0.375	ix.525
25/64						0.390625	nine.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	ten.715625
28/64	xiv/32	7/16				0.4375	11.1125
29/64						0.453125	11.509375
30/64	15/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	4/8	2/4	1/2	0.v	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	18/32	9/16				0.5625	14.2875
37/64						0.578125	fourteen.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	xv.478125
40/64	20/32	10/xvi	five/8			0.625	15.875
41/64						0.640625	sixteen.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	eighteen.653125
48/64	24/32	12/sixteen	half dozen/8	iii/4		0.75	19.05
49/64						0.765625	xix.446875
50/64	25/32					0.78125	nineteen.84375
51/64						0.796875	xx.240625
52/64	26/32	thirteen/16				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/xvi	eight/eight	4/4	2/two	1	25.4