3 3 8 Improper Fraction

Fraction Calculator

Below are multiple fraction calculators capable of improver, subtraction, multiplication, sectionalization, simplification, and conversion between fractions and decimals. Fields higher up the solid black line represent the numerator, while fields below correspond the denominator.

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Mixed Numbers Figurer

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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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Big Number Fraction Figurer

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 total number of parts that make up said whole. For case, in the fraction of

, the numerator is 3, and the denominator is eight. A more illustrative example could involve a pie with viii slices. 1 of those viii slices would constitute the numerator of a fraction, while the full 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

as shown in the image to the correct. Note that the denominator of a fraction cannot exist 0, as it would make the fraction undefined. Fractions can undergo many dissimilar operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such every bit 2 and 8, fractions crave a mutual 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 sure to be a multiple of each private denominator. The numerators also need to be multiplied past the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest mode to ensure that the fractions accept a common denominator. However, in well-nigh cases, the solutions to these equations will not announced in simplified form (the provided reckoner computes the simplification automatically). Beneath is an instance using this method.

This process can exist used for whatsoever 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 problem.

An culling method for finding a mutual denominator is to decide the least common multiple (LCM) for the denominators, and then add or subtract the numerators as one would an integer. Using the least common multiple can be more than efficient and is more than likely to result in a fraction in simplified form. In the example higher up, the denominators were four, 6, and 2. The least common multiple is the first shared multiple of these iii numbers.

Multiples of 2: 2, four, 6, 8 ten, 12

Multiples of 4: 4, 8, 12

Multiples of 6: 6, 12

The start multiple they all share is 12, and then 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 whatever value will make the denominators 12, then add together 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 add-on section equally well as the equations below for description.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in society to multiply fractions. Simply, 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 description.

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 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 work with simplified fractions. Equally such, fraction solutions are ordinarily expressed in their simplified forms.

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form also equally mixed number course. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest mutual 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 point represents a power of 10; the first decimal place being ten^ane, the 2nd 10ⁱⁱ, the third 10^three, and then on. Only make up one's mind what power of ten the decimal extends to, use that power of ten as the denominator, enter each number to the right of the decimal point equally the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10^four, or 10,000. This would make the fraction

, which simplifies to

, since the greatest common cistron between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) tin can be translated to decimal course 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 outset decimal place represents x^-1,

can exist converted to 0.5. If the fraction were instead

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

Common Engineering Fraction to Decimal Conversions

In applied science, fractions are widely used to depict the size of components such as pipes and bolts. The nigh common fractional and decimal equivalents are listed beneath.

64^th	32^nd	16^th	8^th	iv^th	2^nd	Decimal	Decimal (inch to mm)
ane/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	2/32	1/16				0.0625	ane.5875
5/64						0.078125	1.984375
6/64	3/32					0.09375	2.38125
7/64						0.109375	2.778125
8/64	iv/32	2/sixteen	ane/8			0.125	3.175
nine/64						0.140625	3.571875
10/64	5/32					0.15625	3.96875
xi/64						0.171875	4.365625
12/64	6/32	iii/16				0.1875	iv.7625
13/64						0.203125	v.159375
xiv/64	7/32					0.21875	5.55625
fifteen/64						0.234375	5.953125
16/64	eight/32	4/16	ii/viii	1/four		0.25	half-dozen.35
17/64						0.265625	6.746875
eighteen/64	ix/32					0.28125	7.14375
xix/64						0.296875	seven.540625
20/64	10/32	5/16				0.3125	7.9375
21/64						0.328125	8.334375
22/64	xi/32					0.34375	viii.73125
23/64						0.359375	9.128125
24/64	12/32	6/xvi	3/eight			0.375	9.525
25/64						0.390625	nine.921875
26/64	xiii/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	14/32	7/xvi				0.4375	11.1125
29/64						0.453125	11.509375
xxx/64	15/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	4/viii	2/4	1/2	0.v	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	18/32	9/16				0.5625	xiv.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	xv.478125
40/64	20/32	ten/16	5/8			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	11/xvi				0.6875	17.4625
45/64						0.703125	17.859375
46/64	23/32					0.71875	xviii.25625
47/64						0.734375	eighteen.653125
48/64	24/32	12/16	6/8	3/4		0.75	19.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	nineteen.84375
51/64						0.796875	twenty.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/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	30/32	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	16/16	viii/8	4/4	2/2	one	25.4