9 16 Plus 1 2

Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields in a higher place the solid blackness line represent the numerator, while fields beneath stand for 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 Calculator

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Large Number Fraction Calculator

Utilize 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 office 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 brand up said whole. For example, 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 exist 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 right. Note that the denominator of a fraction cannot be 0, as it would brand the fraction undefined. Fractions can undergo many different operations, some of which are mentioned beneath.

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 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 sure to be a multiple of each private denominator. The numerators also need to be multiplied past the appropriate factors to preserve the value of the fraction every bit a whole. This is arguably the simplest way to ensure that the fractions take a mutual denominator. However, in nearly cases, the solutions to these equations will not announced in simplified form (the provided reckoner computes the simplification automatically). Below is an example using this method.

This procedure tin be used for whatsoever number of fractions. Merely 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 own corresponding denominator) in the problem.

An alternative method for finding a mutual denominator is to determine the to the lowest degree common 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 efficient and is more likely to result in a fraction in simplified form. In the instance above, the denominators were 4, half dozen, and two. The least mutual multiple is the first shared multiple of these three numbers.

Multiples of 2: ii, 4, 6, eight ten, 12

Multiples of four: 4, eight, 12

Multiples of 6: half dozen, 12

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

Subtraction:

Fraction subtraction is essentially the same as fraction improver. A common denominator is required for the performance to occur. Refer to the addition section as well as the equations beneath for clarification.

Multiplication:

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

Division:

The procedure for dividing fractions is like to that for multiplying fractions. In gild 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 beneath for clarification.

Simplification:

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

for case, is more than cumbersome than

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

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal identify to the right of the decimal point represents a power of x; the get-go decimal place being 10^one, the second 10², the third 10³, and and then on. Simply determine what power of 10 the decimal extends to, use that ability of 10 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 fourth decimal place, which constitutes ten⁴, or 10,000. This would make the fraction

, which simplifies to

, since the greatest common cistron between the numerator and denominator is ii.

Similarly, fractions with denominators that are powers of ten (or can 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, first convert it into the fraction of

. Knowing that the beginning decimal place represents 10^-one,

can exist 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 division.

Common Engineering science 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	16^th	eight^th	iv^th	ii^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	one/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	ii/32	one/xvi				0.0625	1.5875
five/64						0.078125	1.984375
6/64	3/32					0.09375	ii.38125
7/64						0.109375	2.778125
8/64	four/32	2/16	1/8			0.125	3.175
nine/64						0.140625	3.571875
ten/64	5/32					0.15625	3.96875
xi/64						0.171875	4.365625
12/64	half-dozen/32	3/16				0.1875	4.7625
thirteen/64						0.203125	five.159375
14/64	7/32					0.21875	5.55625
15/64						0.234375	v.953125
16/64	eight/32	4/xvi	2/8	one/iv		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
xix/64						0.296875	seven.540625
20/64	10/32	5/16				0.3125	7.9375
21/64						0.328125	viii.334375
22/64	eleven/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	6/16	3/8			0.375	ix.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	x.715625
28/64	fourteen/32	7/16				0.4375	eleven.1125
29/64						0.453125	xi.509375
xxx/64	15/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	xvi/32	eight/16	4/eight	2/4	i/two	0.5	12.7
33/64						0.515625	xiii.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	18/32	ix/16				0.5625	14.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	xv.478125
forty/64	20/32	ten/16	5/eight			0.625	15.875
41/64						0.640625	xvi.271875
42/64	21/32					0.65625	xvi.66875
43/64						0.671875	17.065625
44/64	22/32	xi/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	vi/8	3/4		0.75	19.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
52/64	26/32	13/xvi				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	7/8			0.875	22.225
57/64						0.890625	22.621875
58/64	29/32					0.90625	23.01875
59/64						0.921875	23.415625
sixty/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	8/8	4/4	2/two	i	25.4

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Source: https://www.calculator.net/fraction-calculator.html

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