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Fraction Figurer

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 beneath represent the denominator.

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Mixed Numbers Calculator

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Simplify Fractions Calculator

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Decimal to Fraction Calculator

Upshot

Calculation steps:

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Fraction to Decimal Calculator

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Big Number Fraction Computer

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 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 upwards said whole. For example, in the fraction of

, the numerator is 3, and the denominator is viii. A more illustrative instance could involve a pie with viii slices. ane of those viii slices would constitute the numerator of a fraction, while the full of 8 slices that comprises the whole pie would exist the denominator. If a person were to swallow 3 slices, the remaining fraction of the pie would therefore exist

as shown in the image to the right. Annotation that the denominator of a fraction cannot exist 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as ii and 8, fractions crave a mutual 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 production 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 also need to be multiplied by the appropriate factors to preserve the value of the fraction equally a whole. This is arguably the simplest mode to ensure that the fractions take a common denominator. Nevertheless, in nearly cases, the solutions to these equations volition not announced in simplified form (the provided computer 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 own respective denominator) in the trouble.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, and so add together or decrease the numerators every bit one would an integer. Using the least common multiple tin can be more efficient and is more likely to result in a fraction in simplified form. In the instance higher up, the denominators were iv, vi, and ii. The least common multiple is the offset shared multiple of these three numbers.

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

Multiples of 4: iv, 8, 12

Multiples of six: six, 12

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

Subtraction:

Fraction subtraction is essentially the aforementioned as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Dissimilar calculation and subtracting, information technology is not necessary to compute a mutual denominator in club to multiply fractions. Only, 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 process for dividing fractions is similar 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 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 be

. Refer to the equations beneath for clarification.

Simplification:

It 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 computer provided returns fraction inputs in both improper fraction course as well equally mixed number form. In both cases, fractions are presented in their everyman forms by dividing both numerator and denominator past their greatest common cistron.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. Information technology does, however, require the agreement that each decimal identify to the right of the decimal point represents a ability of 10; the get-go decimal place beingness 10¹, the second ten², the third ten^three, and then on. Simply determine what ability of ten the decimal extends to, use that power of x 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 4 is in the fourth decimal place, which constitutes 10^four, or 10,000. This would make the fraction

, which simplifies to

, since the greatest mutual factor between the numerator and denominator is ii.

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

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

. Knowing that the offset decimal identify represents x^-1,

can be converted to 0.5. If the fraction were instead

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

Common Engineering Fraction to Decimal Conversions

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

64^th	32^nd	16^th	eight^th	iv^th	ii^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
two/64	one/32					0.03125	0.79375
3/64						0.046875	1.190625
iv/64	2/32	1/xvi				0.0625	ane.5875
5/64						0.078125	ane.984375
6/64	3/32					0.09375	2.38125
7/64						0.109375	two.778125
eight/64	4/32	two/16	1/viii			0.125	iii.175
9/64						0.140625	3.571875
ten/64	v/32					0.15625	3.96875
eleven/64						0.171875	4.365625
12/64	half dozen/32	3/16				0.1875	4.7625
13/64						0.203125	5.159375
14/64	7/32					0.21875	v.55625
15/64						0.234375	5.953125
16/64	8/32	4/16	two/8	i/four		0.25	vi.35
17/64						0.265625	6.746875
eighteen/64	9/32					0.28125	vii.14375
19/64						0.296875	7.540625
20/64	10/32	5/16				0.3125	7.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	viii.73125
23/64						0.359375	ix.128125
24/64	12/32	6/16	iii/viii			0.375	9.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	ten.715625
28/64	xiv/32	7/16				0.4375	eleven.1125
29/64						0.453125	eleven.509375
30/64	15/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	viii/16	4/8	2/4	1/2	0.5	12.7
33/64						0.515625	xiii.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	thirteen.890625
36/64	eighteen/32	9/16				0.5625	14.2875
37/64						0.578125	fourteen.684375
38/64	xix/32					0.59375	15.08125
39/64						0.609375	15.478125
xl/64	20/32	10/sixteen	5/8			0.625	xv.875
41/64						0.640625	xvi.271875
42/64	21/32					0.65625	sixteen.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	18.653125
48/64	24/32	12/16	6/8	3/4		0.75	19.05
49/64						0.765625	xix.446875
50/64	25/32					0.78125	19.84375
51/64						0.796875	xx.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	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	sixteen/16	8/8	iv/4	2/ii	i	25.4