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Fraction Figurer

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, 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 Computer

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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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Large Number Fraction Estimator

Use this computer 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 upwardly said whole. For example, in the fraction of

, the numerator is 3, and the denominator is viii. A more than illustrative example could involve a pie with 8 slices. ane of those 8 slices would establish 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 be

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

Improver:

Unlike adding and subtracting integers such as two and 8, 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 past 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 likewise need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest style to ensure that the fractions have a common denominator. Nonetheless, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process tin can be used for any number of fractions. Merely 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 corresponding denominator) in the trouble.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators every bit 1 would an integer. Using the least mutual multiple can be more efficient and is more likely to result in a fraction in simplified form. In the instance above, the denominators were 4, 6, and two. The to the lowest degree common multiple is the first shared multiple of these three numbers.

Multiples of two: 2, 4, 6, 8 x, 12

Multiples of 4: 4, viii, 12

Multiples of 6: 6, 12

The outset multiple they all share is 12, and then this is the least mutual multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by any value will make the denominators 12, so add the numerators.

Subtraction:

Fraction subtraction is essentially the same equally fraction addition. A common denominator is required for the functioning to occur. Refer to the improver department as well equally 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 order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the outcome forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Sectionalization:

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 only

. 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 description.

Simplification:

It is oft 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 grade as well equally mixed number form. In both cases, fractions are presented in their lowest forms past dividing both numerator and denominator by their greatest mutual gene.

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 bespeak represents a power of 10; the first decimal place beingness x^one, the second 10², the third x^three, and and so on. Simply determine what power of 10 the decimal extends to, use that ability 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 fourth decimal identify, which constitutes x⁴, or 10,000. This would make the fraction

, which simplifies to

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

Similarly, fractions with denominators that are powers of ten (or tin can exist converted to powers of 10) can be 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 first decimal place represents 10^-1,

can exist converted to 0.v. 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 segmentation.

Common Applied science Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such every bit pipes and bolts. The about common fractional and decimal equivalents are listed beneath.

64^th	32^nd	16^th	eight^th	4^th	ii^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
two/64	one/32					0.03125	0.79375
3/64						0.046875	one.190625
4/64	2/32	1/16				0.0625	1.5875
5/64						0.078125	1.984375
six/64	3/32					0.09375	2.38125
seven/64						0.109375	2.778125
8/64	4/32	ii/16	1/8			0.125	3.175
9/64						0.140625	3.571875
10/64	five/32					0.15625	3.96875
11/64						0.171875	4.365625
12/64	6/32	three/16				0.1875	four.7625
13/64						0.203125	5.159375
14/64	seven/32					0.21875	5.55625
15/64						0.234375	5.953125
16/64	8/32	4/16	2/8	1/four		0.25	vi.35
17/64						0.265625	vi.746875
18/64	nine/32					0.28125	7.14375
19/64						0.296875	7.540625
20/64	10/32	5/16				0.3125	vii.9375
21/64						0.328125	eight.334375
22/64	11/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	6/xvi	3/8			0.375	9.525
25/64						0.390625	9.921875
26/64	thirteen/32					0.40625	x.31875
27/64						0.421875	10.715625
28/64	14/32	vii/16				0.4375	11.1125
29/64						0.453125	11.509375
30/64	15/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	16/32	viii/16	iv/8	ii/iv	1/2	0.5	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	xiii.49375
35/64						0.546875	13.890625
36/64	18/32	9/16				0.5625	14.2875
37/64						0.578125	14.684375
38/64	xix/32					0.59375	xv.08125
39/64						0.609375	xv.478125
40/64	xx/32	10/16	v/8			0.625	15.875
41/64						0.640625	xvi.271875
42/64	21/32					0.65625	16.66875
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	12/16	6/8	3/four		0.75	19.05
49/64						0.765625	19.446875
l/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
52/64	26/32	thirteen/16				0.8125	twenty.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/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	8/8	four/4	2/2	1	25.4

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

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