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Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, segmentation, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below 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

Result

Adding steps:

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Fraction to Decimal Calculator

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Large Number Fraction Calculator

Use 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 example, in the fraction of

, the numerator is 3, and the denominator is eight. A more illustrative case could involve a pie with eight slices. i 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 3 slices, the remaining fraction of the pie would therefore be

equally shown in the image to the right. Annotation 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.

Addition:

Unlike adding and subtracting integers such as 2 and eight, 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 individual denominator. The numerators likewise 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. However, in near cases, the solutions to these equations volition not appear in simplified form (the provided reckoner computes the simplification automatically). Below is an case using this method.

This process tin can exist used for whatever number of fractions. Merely multiply the numerators and denominators of each fraction in the problem by the production of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An culling method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add together or subtract the numerators as one would an integer. Using the least common multiple tin can be more efficient and is more likely to effect in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the get-go shared multiple of these 3 numbers.

Multiples of 2: 2, iv, six, 8 10, 12

Multiples of iv: iv, viii, 12

Multiples of 6: six, 12

The first multiple they all share is 12, then this is the to the lowest degree common multiple. To complete an addition (or subtraction) trouble, multiply the numerators and denominators of each fraction in the trouble past whatever value will brand the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is substantially the aforementioned as fraction addition. A common denominator is required for the operation to occur. Refer to the addition department equally well every bit the equations beneath for clarification.

Multiplication:

Multiplying fractions is adequately straightforward. Unlike adding and subtracting, information technology is not necessary to compute a mutual denominator in order to multiply fractions. Only, the numerators and denominators of each fraction are multiplied, and the effect forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for description.

Division:

The process for dividing fractions is similar to that for multiplying fractions. In guild 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 below for clarification.

Simplification:

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

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form also every bit mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common gene.

Converting betwixt fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal signal represents a power of 10; the beginning decimal place being 10¹, the 2nd ten², the third 10^three, and so on. Simply determine what power of 10 the decimal extends to, employ that power of 10 equally the denominator, enter each number to the correct of the decimal point as the numerator, and simplify. For case, looking at the number 0.1234, the number iv is in the fourth decimal place, which constitutes 10⁴, or x,000. This would brand 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 can be converted to powers of 10) can be translated to decimal class using the same principles. Take the fraction

for case. To convert this fraction into a decimal, outset convert information technology into the fraction of

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

can be converted to 0.5. If the fraction were instead

, the decimal would and so exist 0.05, and so on. Beyond this, converting fractions into decimals requires the functioning of long sectionalization.

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 fractional and decimal equivalents are listed beneath.

64th	32nd	16th	viiithursday	4thursday	2nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	i/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	2/32	1/16				0.0625	1.5875
5/64						0.078125	1.984375
half-dozen/64	3/32					0.09375	2.38125
7/64						0.109375	two.778125
viii/64	4/32	2/16	i/8			0.125	3.175
nine/64						0.140625	3.571875
10/64	5/32					0.15625	3.96875
11/64						0.171875	iv.365625
12/64	vi/32	3/16				0.1875	4.7625
13/64						0.203125	5.159375
14/64	vii/32					0.21875	v.55625
15/64						0.234375	v.953125
16/64	viii/32	4/16	2/8	1/iv		0.25	vi.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	vii.14375
19/64						0.296875	7.540625
20/64	10/32	5/xvi				0.3125	7.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	half dozen/xvi	3/eight			0.375	9.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	14/32	vii/xvi				0.4375	xi.1125
29/64						0.453125	xi.509375
30/64	fifteen/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	iv/8	2/4	1/two	0.5	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	xiv.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	15.478125
40/64	20/32	10/16	5/8			0.625	15.875
41/64						0.640625	16.271875
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	18.653125
48/64	24/32	12/sixteen	6/viii	iii/4		0.75	19.05
49/64						0.765625	nineteen.446875
50/64	25/32					0.78125	19.84375
51/64						0.796875	twenty.240625
52/64	26/32	13/16				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/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	thirty/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/8	4/4	two/2	1	25.4