2 Thirds Divided By 2

Fraction Calculator

Beneath are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields higher up the solid blackness line represent the numerator, while fields below represent the denominator.

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Mixed Numbers Figurer

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Simplify Fractions Computer

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Decimal to Fraction Calculator

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Fraction to Decimal Computer

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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 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 up said whole. For instance, in the fraction of

, the numerator is 3, and the denominator is 8. A more than illustrative case could involve a pie with eight slices. one of those 8 slices would constitute the numerator of a fraction, while the total of eight slices that comprises the whole pie would be the denominator. If a person were to eat three slices, the remaining fraction of the pie would therefore be

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

Addition:

Dissimilar adding and subtracting integers such as ii and 8, fractions require a common denominator to undergo these operations. Ane method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved past 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 also 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 nearly cases, the solutions to these equations will not appear in simplified grade (the provided computer computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem past the product 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 decide the least common multiple (LCM) for the denominators, and so add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example to a higher place, the denominators were four, half-dozen, and 2. The least common multiple is the start shared multiple of these three numbers.

Multiples of 2: ii, 4, half dozen, eight 10, 12

Multiples of 4: 4, 8, 12

Multiples of 6: 6, 12

The first multiple they all share is 12, and then this is the least common multiple. To complete an improver (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by any value volition brand the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is substantially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the improver department likewise as the equations below for description.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike calculation and subtracting, information technology is non necessary to compute a common denominator in order to multiply fractions. Just, 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 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 but

. 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. Every bit such, fraction solutions are normally expressed in their simplified forms.

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction grade every bit well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common 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 right of the decimal betoken represents a power of x; the starting time decimal place being 10¹, the 2nd x², the third 10³, and and so on. But make up one's mind what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal indicate as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the 4th decimal place, which constitutes 10^four, or 10,000. This would brand 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 exist converted to powers of 10) tin can be translated to decimal form using the same principles. Take the fraction

for example. To convert this fraction into a decimal, commencement convert it into the fraction of

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

tin can exist converted to 0.5. If the fraction were instead

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

Common Engineering Fraction to Decimal Conversions

In applied science, fractions are widely used to describe the size of components such every bit pipes and bolts. The most common partial and decimal equivalents are listed below.

64^th	32^nd	16^th	eight^th	iv^thursday	2^nd	Decimal	Decimal (inch to mm)
i/64						0.015625	0.396875
two/64	1/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	2/32	i/16				0.0625	1.5875
v/64						0.078125	1.984375
6/64	three/32					0.09375	2.38125
7/64						0.109375	2.778125
viii/64	4/32	two/16	i/8			0.125	3.175
9/64						0.140625	3.571875
x/64	5/32					0.15625	3.96875
eleven/64						0.171875	four.365625
12/64	half dozen/32	3/16				0.1875	4.7625
13/64						0.203125	5.159375
14/64	7/32					0.21875	five.55625
15/64						0.234375	five.953125
xvi/64	viii/32	four/16	2/8	i/4		0.25	6.35
17/64						0.265625	6.746875
eighteen/64	9/32					0.28125	7.14375
19/64						0.296875	seven.540625
20/64	ten/32	v/16				0.3125	7.9375
21/64						0.328125	8.334375
22/64	eleven/32					0.34375	eight.73125
23/64						0.359375	9.128125
24/64	12/32	half dozen/16	3/eight			0.375	ix.525
25/64						0.390625	nine.921875
26/64	13/32					0.40625	x.31875
27/64						0.421875	x.715625
28/64	fourteen/32	7/xvi				0.4375	11.1125
29/64						0.453125	eleven.509375
thirty/64	15/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	16/32	viii/16	iv/viii	2/4	1/2	0.5	12.7
33/64						0.515625	thirteen.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	thirteen.890625
36/64	18/32	9/sixteen				0.5625	14.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	fifteen.08125
39/64						0.609375	xv.478125
twoscore/64	20/32	10/16	5/8			0.625	fifteen.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	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	nineteen.446875
50/64	25/32					0.78125	xix.84375
51/64						0.796875	twenty.240625
52/64	26/32	thirteen/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	14/16	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	xxx/32	15/xvi				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	xvi/16	8/8	4/4	2/2	1	25.4