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Fraction Reckoner

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

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Mixed Numbers Reckoner

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Simplify Fractions Estimator

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Decimal to Fraction Estimator

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Fraction to Decimal Calculator

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Large Number Fraction Estimator

Use this estimator if the numerators or denominators are very big integers.

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In mathematics, a fraction is a number that represents a function 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 up said whole. For instance, in the fraction of

, the numerator is three, and the denominator is 8. A more illustrative example could involve a pie with eight slices. ane 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 eat 3 slices, the remaining fraction of the pie would therefore exist

every bit shown in the image to the correct. Notation that the denominator of a fraction cannot be 0, as it would brand the fraction undefined. Fractions tin undergo many unlike operations, some of which are mentioned beneath.

Improver:

Unlike calculation and subtracting integers such as two and 8, fractions require a mutual denominator to undergo these operations. 1 method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved past the production 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 likewise demand to be multiplied by the appropriate factors to preserve the value of the fraction equally a whole. This is arguably the simplest fashion to ensure that the fractions have a mutual denominator. However, in most cases, the solutions to these equations will not appear in simplified grade (the provided estimator computes the simplification automatically). Below is an instance using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the trouble past the production of the denominators of all the other fractions (not including its ain respective denominator) in the problem.

An alternative method for finding a common denominator is to decide the least mutual multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more than efficient and is more likely to result in a fraction in simplified grade. In the example above, the denominators were iv, 6, and 2. The to the lowest degree mutual multiple is the offset shared multiple of these 3 numbers.

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

Multiples of 4: iv, 8, 12

Multiples of 6: half dozen, 12

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

Subtraction:

Fraction subtraction is essentially the aforementioned as fraction add-on. A common denominator is required for the performance to occur. Refer to the addition department as well as the equations beneath for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not 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 exist simplified. Refer to the equations beneath for clarification.

Division:

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

Information technology is often easier to work with simplified fractions. As 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 form equally well equally mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator past their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, nonetheless, require the understanding that each decimal identify to the correct of the decimal signal represents a ability of 10; the beginning decimal identify being x¹, the second 10^two, the tertiary 10³, so on. Just determine what ability of 10 the decimal extends to, utilise that power of ten every bit 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 fourth decimal identify, which constitutes ten⁴, or 10,000. This would brand the fraction

, which simplifies to

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

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

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

. Knowing that the first decimal place represents 10^-one,

can be converted to 0.5. If the fraction were instead

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

Mutual Engineering Fraction to Decimal Conversions

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

64^th	32^nd	16^th	8^thursday	four^th	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
three/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	2.778125
8/64	4/32	2/16	1/8			0.125	3.175
9/64						0.140625	iii.571875
10/64	5/32					0.15625	three.96875
eleven/64						0.171875	iv.365625
12/64	half-dozen/32	3/16				0.1875	4.7625
13/64						0.203125	5.159375
14/64	7/32					0.21875	5.55625
15/64						0.234375	5.953125
16/64	8/32	4/16	two/eight	1/4		0.25	six.35
17/64						0.265625	6.746875
eighteen/64	9/32					0.28125	7.14375
19/64						0.296875	7.540625
20/64	10/32	v/sixteen				0.3125	seven.9375
21/64						0.328125	eight.334375
22/64	xi/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	6/16	three/viii			0.375	ix.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	ten.715625
28/64	14/32	7/sixteen				0.4375	11.1125
29/64						0.453125	eleven.509375
30/64	xv/32					0.46875	eleven.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	4/8	2/4	one/two	0.v	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	nine/sixteen				0.5625	14.2875
37/64						0.578125	14.684375
38/64	nineteen/32					0.59375	15.08125
39/64						0.609375	xv.478125
40/64	20/32	ten/16	v/8			0.625	15.875
41/64						0.640625	16.271875
42/64	21/32					0.65625	16.66875
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	half dozen/eight	3/4		0.75	19.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
52/64	26/32	13/sixteen				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	7/8			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	xvi/16	8/8	four/iv	2/2	ane	25.4

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Source: https://www.calculator.net/fraction-calculator.html

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