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Fraction Computer

Below are multiple fraction calculators capable of improver, subtraction, multiplication, division, simplification, and conversion betwixt fractions and decimals. Fields above the solid blackness 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

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Fraction to Decimal Calculator

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Big 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 role 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 8. A more illustrative case could involve a pie with eight slices. one of those 8 slices would establish 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 iii 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 tin can undergo many unlike operations, some of which are mentioned below.

Addition:

Unlike calculation and subtracting integers such every bit 2 and eight, fractions require a common denominator to undergo these operations. I method for finding a common 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 be a multiple of each individual denominator. The numerators besides need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest manner to ensure that the fractions have a common denominator. Still, in most cases, the solutions to these equations will not announced in simplified class (the provided calculator computes the simplification automatically). Below is an instance using this method.

This process can be used for whatsoever number of fractions. Just 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 trouble.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, so add together or subtract the numerators as one would an integer. Using the to the lowest degree mutual multiple can exist more than efficient and is more likely to result in a fraction in simplified class. In the instance above, the denominators were 4, six, and 2. The least common multiple is the first shared multiple of these three numbers.

Multiples of ii: 2, 4, vi, 8 10, 12

Multiples of 4: 4, eight, 12

Multiples of six: 6, 12

The starting time multiple they all share is 12, and so 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 brand the denominators 12, so add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A mutual denominator is required for the operation to occur. Refer to the improver section also as the equations beneath for description.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike calculation and subtracting, it is not necessary to compute a common 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 be simplified. Refer to the equations beneath for description.

Segmentation:

The process for dividing fractions is similar to that for multiplying fractions. In order to separate 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 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:

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

for case, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form also as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator past their greatest mutual factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the correct of the decimal point represents a power of 10; the get-go decimal place being x¹, the second 10ⁱⁱ, the third 10^three, and so on. Simply decide what power of ten the decimal extends to, use that power of 10 every bit 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 4 is in the fourth decimal place, which constitutes 10⁴, or 10,000. This would make the fraction

, which simplifies to

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

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

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

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

can be converted to 0.5. If the fraction were instead

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

Common Technology Fraction to Decimal Conversions

In engineering, fractions are widely used to draw the size of components such every bit pipes and bolts. The almost common partial and decimal equivalents are listed below.

64th	32nd	16th	8th	ivth	iind	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
3/64						0.046875	ane.190625
4/64	2/32	ane/16				0.0625	1.5875
5/64						0.078125	i.984375
6/64	3/32					0.09375	2.38125
seven/64						0.109375	2.778125
8/64	4/32	2/16	1/viii			0.125	3.175
nine/64						0.140625	three.571875
10/64	5/32					0.15625	3.96875
xi/64						0.171875	4.365625
12/64	6/32	3/sixteen				0.1875	iv.7625
13/64						0.203125	v.159375
fourteen/64	7/32					0.21875	5.55625
15/64						0.234375	v.953125
16/64	8/32	four/xvi	ii/viii	1/4		0.25	6.35
17/64						0.265625	6.746875
18/64	nine/32					0.28125	7.14375
nineteen/64						0.296875	7.540625
twenty/64	10/32	five/16				0.3125	vii.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/eight			0.375	9.525
25/64						0.390625	9.921875
26/64	xiii/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	14/32	7/sixteen				0.4375	xi.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	8/16	4/8	ii/4	1/2	0.five	12.vii
33/64						0.515625	thirteen.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	18/32	9/xvi				0.5625	xiv.2875
37/64						0.578125	14.684375
38/64	nineteen/32					0.59375	15.08125
39/64						0.609375	15.478125
40/64	20/32	ten/16	5/8			0.625	15.875
41/64						0.640625	sixteen.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	eighteen.25625
47/64						0.734375	18.653125
48/64	24/32	12/16	vi/8	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	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	14/sixteen	vii/viii			0.875	22.225
57/64						0.890625	22.621875
58/64	29/32					0.90625	23.01875
59/64						0.921875	23.415625
threescore/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	viii/viii	4/four	two/2	1	25.iv