6 6/10 Divided By 6

Fraction Calculator

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

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Mixed Numbers Calculator

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Simplify Fractions Figurer

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Decimal to Fraction Computer

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Fraction to Decimal Calculator

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Big Number Fraction Reckoner

Use this calculator if the numerators or denominators are very large integers.

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In mathematics, a fraction is a number that represents a office 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 brand upwardly said whole. For example, in the fraction of

, the numerator is three, and the denominator is 8. A more illustrative instance could involve a pie with 8 slices. 1 of those 8 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 eat three slices, the remaining fraction of the pie would therefore be

as shown in the image 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 below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. 1 method for finding a common 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 sure to be a multiple of each private denominator. The numerators too 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 class (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 (non including its own respective denominator) in the problem.

An alternative method for finding a mutual denominator is to decide the least mutual multiple (LCM) for the denominators, then add together or subtract the numerators as one would an integer. Using the least mutual multiple can be more than efficient and is more than likely to effect in a fraction in simplified form. In the case above, the denominators were four, half dozen, and 2. The least common multiple is the first shared multiple of these three numbers.

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

Multiples of iv: 4, 8, 12

Multiples of half dozen: 6, 12

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

Subtraction:

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

Multiplication:

Multiplying fractions is adequately straightforward. Unlike adding and subtracting, it is not necessary to compute a mutual 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 procedure for dividing fractions is like 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 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:

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

for example, is more cumbersome than

. The reckoner provided returns fraction inputs in both improper fraction grade equally well as 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, even so, require the understanding that each decimal place to the right of the decimal point represents a power of x; the first decimal place beingness ten¹, the second 10^two, the tertiary xⁱⁱⁱ, and so on. Just decide what power of x the decimal extends to, apply that power of 10 equally the denominator, enter each number to the right of the decimal point every bit the numerator, and simplify. For instance, looking at the number 0.1234, the number iv is in the fourth decimal place, which constitutes 10⁴, or 10,000. This would brand the fraction

, which simplifies to

, since the greatest common cistron betwixt the numerator and denominator is 2.

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

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

. Knowing that the start decimal place represents 10^-1,

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

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

Mutual Engineering Fraction to Decimal Conversions

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

64^thursday	32^nd	16^thursday	8^th	4^th	two^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
iii/64						0.046875	1.190625
4/64	2/32	1/16				0.0625	ane.5875
5/64						0.078125	one.984375
6/64	3/32					0.09375	two.38125
7/64						0.109375	2.778125
8/64	iv/32	two/16	1/8			0.125	three.175
9/64						0.140625	3.571875
ten/64	five/32					0.15625	three.96875
eleven/64						0.171875	4.365625
12/64	6/32	three/xvi				0.1875	iv.7625
xiii/64						0.203125	5.159375
14/64	seven/32					0.21875	five.55625
xv/64						0.234375	v.953125
sixteen/64	viii/32	4/16	ii/viii	ane/4		0.25	half-dozen.35
17/64						0.265625	6.746875
18/64	ix/32					0.28125	7.14375
nineteen/64						0.296875	7.540625
20/64	10/32	5/sixteen				0.3125	7.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	eight.73125
23/64						0.359375	ix.128125
24/64	12/32	half-dozen/16	3/eight			0.375	9.525
25/64						0.390625	9.921875
26/64	thirteen/32					0.40625	x.31875
27/64						0.421875	10.715625
28/64	14/32	seven/sixteen				0.4375	11.1125
29/64						0.453125	11.509375
30/64	xv/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	4/8	two/four	1/ii	0.five	12.vii
33/64						0.515625	13.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	thirteen.890625
36/64	18/32	9/xvi				0.5625	xiv.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	15.478125
xl/64	twenty/32	10/xvi	5/8			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	12/16	half dozen/viii	iii/4		0.75	19.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	nineteen.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	14/16	7/eight			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	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/sixteen	viii/eight	four/4	2/2	1	25.4