1/6 X 3/4 In Fraction

Fraction Calculator

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

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Mixed Numbers Calculator

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Simplify Fractions Calculator

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Decimal to Fraction Computer

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Fraction to Decimal Estimator

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Big Number Fraction Calculator

Use this reckoner 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 example, in the fraction of

, the numerator is 3, and the denominator is viii. A more illustrative example could involve a pie with 8 slices. 1 of those 8 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 be

as shown in the image to the right. Note that the denominator of a fraction cannot exist 0, as information technology would make the fraction undefined. Fractions tin undergo many different operations, some of which are mentioned below.

Addition:

Different adding and subtracting integers such as two and viii, fractions crave 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 by 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 private denominator. The numerators also demand 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 mutual denominator. However, in near cases, the solutions to these equations will non appear in simplified form (the provided reckoner 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 by the product of the denominators of all the other fractions (not including its ain respective denominator) in the problem.

An culling method for finding a common denominator is to determine the least mutual multiple (LCM) for the denominators, then add or subtract the numerators every bit one would an integer. Using the to the lowest degree mutual multiple tin can be more efficient and is more probable to result in a fraction in simplified form. In the example higher up, the denominators were 4, half dozen, and 2. The least common multiple is the first shared multiple of these three numbers.

Multiples of 2: 2, iv, 6, eight x, 12

Multiples of 4: iv, 8, 12

Multiples of half dozen: vi, 12

The showtime multiple they all share is 12, so this is the to the lowest degree 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 the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section also every bit the equations beneath for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a mutual denominator in guild 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 clarification.

Division:

The process for dividing fractions is similar to that for multiplying fractions. In order to separate 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 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 frequently easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for case, is more cumbersome than

. The computer provided returns fraction inputs in both improper fraction class as well as mixed number grade. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common gene.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. Information technology does, nonetheless, require the understanding that each decimal place to the correct of the decimal betoken represents a power of ten; the first decimal place being tenⁱ, the second ten^two, the third 10³, and then on. Only determine what power of 10 the decimal extends to, apply that power of x as the denominator, enter each number to the right of the decimal point every bit the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10⁴, or x,000. This would make the fraction

, which simplifies to

, since the greatest common factor 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 exist translated to decimal form using the same principles. Take the fraction

for example. To convert this fraction into a decimal, first convert information technology into the fraction of

. Knowing that the commencement decimal place represents 10^-ane,

tin exist converted to 0.5. If the fraction were instead

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

Common Technology Fraction to Decimal Conversions

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

64^th	32^nd	16^th	8^th	4^thursday	ii^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	one/16				0.0625	1.5875
5/64						0.078125	1.984375
6/64	three/32					0.09375	2.38125
7/64						0.109375	two.778125
8/64	four/32	ii/xvi	i/eight			0.125	3.175
9/64						0.140625	3.571875
x/64	5/32					0.15625	3.96875
11/64						0.171875	4.365625
12/64	half dozen/32	3/16				0.1875	4.7625
thirteen/64						0.203125	five.159375
14/64	7/32					0.21875	5.55625
15/64						0.234375	five.953125
sixteen/64	8/32	4/16	2/8	1/four		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
nineteen/64						0.296875	7.540625
twenty/64	x/32	5/16				0.3125	7.9375
21/64						0.328125	8.334375
22/64	xi/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	half dozen/16	3/8			0.375	nine.525
25/64						0.390625	ix.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	fourteen/32	7/16				0.4375	xi.1125
29/64						0.453125	11.509375
30/64	15/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	8/16	4/8	two/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	thirteen.890625
36/64	18/32	9/16				0.5625	fourteen.2875
37/64						0.578125	fourteen.684375
38/64	xix/32					0.59375	15.08125
39/64						0.609375	fifteen.478125
twoscore/64	20/32	ten/xvi	5/eight			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/sixteen	6/8	3/4		0.75	xix.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	nineteen.84375
51/64						0.796875	xx.240625
52/64	26/32	xiii/xvi				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/sixteen	vii/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	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	iv/4	2/2	one	25.iv