2 3 Times 2 4

Fraction Reckoner

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields to a higher place 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

Upshot

Calculation steps:

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Fraction to Decimal Calculator

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Big Number Fraction Computer

Employ 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. 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 make upward said whole. For example, in the fraction of

, the numerator is 3, and the denominator is eight. A more illustrative example could involve a pie with viii slices. one of those 8 slices would constitute 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 swallow iii slices, the remaining fraction of the pie would therefore be

equally shown in the image to the correct. Note that the denominator of a fraction cannot be 0, every bit 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 viii, fractions require a common denominator to undergo these operations. One 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 too need to exist 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 accept a common denominator. Nonetheless, in near cases, the solutions to these equations will not appear in simplified course (the provided calculator computes the simplification automatically). Below is an example using this method.

This process tin 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 culling method for finding a common denominator is to make up one's mind the least common multiple (LCM) for the denominators, then add together or subtract the numerators as i would an integer. Using the to the lowest degree mutual multiple can exist more efficient and is more than likely to result in a fraction in simplified grade. In the example above, the denominators were four, 6, and ii. The least common multiple is the first shared multiple of these three numbers.

Multiples of 2: 2, 4, half dozen, 8 ten, 12

Multiples of 4: 4, 8, 12

Multiples of half dozen: vi, 12

The beginning multiple they all share is 12, and so this is the least mutual multiple. To complete an add-on (or subtraction) trouble, multiply the numerators and denominators of each fraction in the problem by whatever value volition make the denominators 12, so add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition department too every bit the equations below for clarification.

Multiplication:

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

Division:

The process for dividing fractions is like to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied past 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:

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

for instance, is more cumbersome than

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

Converting betwixt fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, crave the understanding that each decimal identify to the correct of the decimal indicate represents a ability of 10; the offset decimal place being ten¹, the second x², the third 10^three, and and then on. Only determine what ability of 10 the decimal extends to, employ that power of 10 every bit 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 4th decimal place, which constitutes ten⁴, 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 x) can exist translated to decimal form 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 showtime decimal identify represents 10^-i,

can exist converted to 0.v. If the fraction were instead

, the decimal would and then be 0.05, then on. Beyond this, converting fractions into decimals requires the performance of long division.

Common Engineering science Fraction to Decimal Conversions

In applied science, fractions are widely used to describe the size of components such as pipes and bolts. The most mutual fractional and decimal equivalents are listed below.

64^th	32^nd	sixteen^thursday	8^th	4^th	ii^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
ii/64	ane/32					0.03125	0.79375
iii/64						0.046875	1.190625
4/64	2/32	1/16				0.0625	one.5875
5/64						0.078125	1.984375
6/64	three/32					0.09375	2.38125
7/64						0.109375	ii.778125
8/64	4/32	two/16	1/eight			0.125	three.175
nine/64						0.140625	3.571875
ten/64	5/32					0.15625	iii.96875
eleven/64						0.171875	4.365625
12/64	6/32	3/sixteen				0.1875	4.7625
13/64						0.203125	5.159375
fourteen/64	7/32					0.21875	v.55625
15/64						0.234375	5.953125
16/64	8/32	four/16	two/viii	1/iv		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
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	nine.128125
24/64	12/32	half dozen/xvi	3/8			0.375	9.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	x.715625
28/64	14/32	7/16				0.4375	xi.1125
29/64						0.453125	eleven.509375
thirty/64	xv/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	eight/16	iv/8	ii/4	1/2	0.5	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	xiii.49375
35/64						0.546875	xiii.890625
36/64	18/32	9/sixteen				0.5625	fourteen.2875
37/64						0.578125	fourteen.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	xv.478125
40/64	twenty/32	10/sixteen	v/eight			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	xviii.25625
47/64						0.734375	18.653125
48/64	24/32	12/xvi	6/8	three/4		0.75	19.05
49/64						0.765625	xix.446875
50/64	25/32					0.78125	nineteen.84375
51/64						0.796875	twenty.240625
52/64	26/32	13/16				0.8125	xx.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	seven/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	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/xvi	8/8	4/iv	ii/2	1	25.four