3 8 Plus 5 16

Fraction Figurer

Below are multiple fraction calculators capable of addition, subtraction, multiplication, sectionalization, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields beneath 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 Computer

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Big Number Fraction Calculator

Utilize this figurer 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 case, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative instance could involve a pie with 8 slices. 1 of those eight slices would institute 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 3 slices, the remaining fraction of the pie would therefore exist

as shown in the paradigm to the right. Note that the denominator of a fraction cannot be 0, equally it would make the fraction undefined. Fractions can undergo many dissimilar operations, some of which are mentioned beneath.

Addition:

Dissimilar adding and subtracting integers such as 2 and 8, 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 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 also need to exist multiplied past the appropriate 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. However, in about cases, the solutions to these equations will non appear in simplified class (the provided calculator computes the simplification automatically). Beneath 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 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, so add or subtract the numerators as ane would an integer. Using the to the lowest degree common multiple can be more efficient and is more likely to outcome in a fraction in simplified form. In the case above, the denominators were 4, 6, and 2. The least common multiple is the kickoff shared multiple of these three numbers.

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

Multiples of 4: 4, viii, 12

Multiples of six: 6, 12

The kickoff multiple they all share is 12, 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 whatsoever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same every bit fraction add-on. A mutual denominator is required for the performance to occur. Refer to the addition department also every bit the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Different adding and subtracting, it is non necessary to compute a common denominator in order to multiply fractions. Only, 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 below for clarification.

Partitioning:

The procedure for dividing fractions is similar to that for multiplying fractions. In order to split up 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:

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

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction grade as well as mixed number form. In both cases, fractions are presented in their everyman forms by dividing both numerator and denominator past their greatest common cistron.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, withal, require the understanding that each decimal place to the right of the decimal point represents a ability of 10; the first decimal identify being 10^one, the second ten^two, the third x³, and so on. Simply 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 correct of the decimal betoken as the numerator, and simplify. For example, looking at the number 0.1234, the number four is in the 4th decimal identify, 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 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the aforementioned principles. Have 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 ten^-1,

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

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

Common Engineering Fraction to Decimal Conversions

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

64^thursday	32^nd	16^th	8^th	iv^thursday	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
ii/64	1/32					0.03125	0.79375
three/64						0.046875	one.190625
4/64	two/32	1/16				0.0625	1.5875
five/64						0.078125	ane.984375
half dozen/64	3/32					0.09375	2.38125
vii/64						0.109375	2.778125
8/64	4/32	2/xvi	1/8			0.125	3.175
nine/64						0.140625	3.571875
10/64	v/32					0.15625	iii.96875
eleven/64						0.171875	iv.365625
12/64	six/32	iii/16				0.1875	4.7625
thirteen/64						0.203125	5.159375
fourteen/64	7/32					0.21875	5.55625
15/64						0.234375	5.953125
16/64	8/32	iv/16	2/8	one/4		0.25	half-dozen.35
17/64						0.265625	vi.746875
18/64	9/32					0.28125	vii.14375
19/64						0.296875	7.540625
20/64	ten/32	5/xvi				0.3125	seven.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	6/16	iii/viii			0.375	9.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	x.31875
27/64						0.421875	10.715625
28/64	fourteen/32	vii/16				0.4375	eleven.1125
29/64						0.453125	11.509375
thirty/64	xv/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	sixteen/32	8/sixteen	4/8	2/four	1/2	0.5	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	xviii/32	9/sixteen				0.5625	14.2875
37/64						0.578125	14.684375
38/64	xix/32					0.59375	15.08125
39/64						0.609375	15.478125
twoscore/64	xx/32	ten/16	5/8			0.625	xv.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	18.25625
47/64						0.734375	xviii.653125
48/64	24/32	12/16	half dozen/8	3/iv		0.75	19.05
49/64						0.765625	xix.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	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
lx/64	30/32	15/sixteen				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	8/8	four/4	2/ii	1	25.4