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Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, segmentation, simplification, and conversion betwixt fractions and decimals. Fields above the solid blackness line stand for the numerator, while fields beneath represent the denominator.

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Mixed Numbers Calculator

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Simplify Fractions Estimator

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Decimal to Fraction Estimator

Result

Calculation steps:

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Fraction to Decimal Calculator

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Big Number Fraction Calculator

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 full number of parts that make upwardly 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 8 slices. 1 of those 8 slices would institute 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 be

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

Improver:

Different adding and subtracting integers such as two 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 certain to exist a multiple of each individual denominator. The numerators besides need to be multiplied by the advisable factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in near cases, the solutions to these equations volition not appear in simplified grade (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for whatsoever number of fractions. Simply 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 culling method for finding a mutual denominator is to determine the least common multiple (LCM) for the denominators, and then add or subtract the numerators equally one would an integer. Using the to the lowest degree common multiple can be more than efficient and is more than probable to result in a fraction in simplified form. In the example above, the denominators were 4, half-dozen, and two. The least common multiple is the beginning shared multiple of these three numbers.

Multiples of two: 2, 4, six, 8 10, 12

Multiples of four: 4, 8, 12

Multiples of 6: vi, 12

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

Subtraction:

Fraction subtraction is substantially the same as fraction addition. A mutual denominator is required for the operation to occur. Refer to the add-on section too as the equations below for clarification.

Multiplication:

Multiplying fractions is adequately straightforward. Unlike calculation and subtracting, information technology is not necessary to compute a mutual denominator in order to multiply fractions. Merely, 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.

Sectionalization:

The procedure for dividing fractions is similar to that for multiplying fractions. In order to dissever 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 substantially 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:

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

for instance, is more cumbersome than

. The reckoner 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 between fractions and decimals:

Converting from decimals to fractions is straightforward. Information technology does, notwithstanding, require the agreement that each decimal identify to the right of the decimal point represents a power of x; the showtime decimal place being 10¹, the 2nd 10², the 3rd 10³, so on. Simply determine what power of 10 the decimal extends to, employ that ability of ten equally the denominator, enter each number to the correct of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number four is in the fourth decimal place, which constitutes 10^iv, or 10,000. This would make the fraction

, which simplifies to

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

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

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

. Knowing that the starting time decimal place represents x^-i,

tin be converted to 0.5. If the fraction were instead

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

Common Engineering Fraction to Decimal Conversions

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

64^th	32^nd	16^th	8^thursday	4^th	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
two/64	ane/32					0.03125	0.79375
iii/64						0.046875	1.190625
iv/64	ii/32	one/16				0.0625	1.5875
5/64						0.078125	1.984375
six/64	iii/32					0.09375	2.38125
seven/64						0.109375	2.778125
8/64	iv/32	2/16	one/8			0.125	3.175
nine/64						0.140625	3.571875
10/64	v/32					0.15625	iii.96875
11/64						0.171875	4.365625
12/64	6/32	three/sixteen				0.1875	4.7625
13/64						0.203125	5.159375
14/64	seven/32					0.21875	v.55625
15/64						0.234375	five.953125
sixteen/64	8/32	4/16	2/eight	ane/4		0.25	half-dozen.35
17/64						0.265625	6.746875
18/64	nine/32					0.28125	7.14375
19/64						0.296875	vii.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	9.128125
24/64	12/32	6/16	iii/8			0.375	nine.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	seven/sixteen				0.4375	11.1125
29/64						0.453125	11.509375
30/64	15/32					0.46875	eleven.90625
31/64						0.484375	12.303125
32/64	xvi/32	8/16	four/8	2/4	1/2	0.5	12.seven
33/64						0.515625	13.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	xiii.890625
36/64	18/32	ix/16				0.5625	fourteen.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	xv.478125
40/64	20/32	x/xvi	5/8			0.625	15.875
41/64						0.640625	16.271875
42/64	21/32					0.65625	sixteen.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	18.653125
48/64	24/32	12/16	6/8	3/four		0.75	nineteen.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	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	14/sixteen	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	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	16/16	eight/8	iv/4	2/2	1	25.4