1/3 Divided by 7 as a Fraction

Fraction Reckoner

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

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Big Number Fraction Estimator

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 office 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 8. A more illustrative instance could involve a pie with 8 slices. 1 of those 8 slices would institute 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 swallow 3 slices, the remaining fraction of the pie would therefore exist

equally shown in the image to the right. Note that the denominator of a fraction cannot be 0, every bit it would brand the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such equally 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 certain to exist a multiple of each individual 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 way to ensure that the fractions take a common denominator. However, in most cases, the solutions to these equations will not appear in simplified grade (the provided calculator computes the simplification automatically). Beneath is an example using this method.

This process can be used for any number of fractions. Merely multiply the numerators and denominators of each fraction in the problem past the product of the denominators of all the other fractions (not including its own corresponding denominator) in the problem.

An alternative method for finding a common denominator is to make up one’s mind the to the lowest degree common multiple (LCM) for the denominators, then add together or decrease the numerators as one would an integer. Using the least common multiple tin be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, vi, and two. The least common multiple is the starting time shared multiple of these three numbers.

Multiples of 2: 2, 4, 6, 8 10, 12

Multiples of iv: 4, 8, 12

Multiples of 6: 6, 12

The first 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 past whatever value volition 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 equally well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Dissimilar adding and subtracting, information technology is non necessary to compute a common 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 beneath 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 description.

Simplification:

It is often easier to piece of 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 too every bit mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator past their greatest common gene.

Converting betwixt fractions and decimals:

Converting from decimals to fractions is straightforward. Information technology does, however, require the understanding that each decimal identify to the correct of the decimal point represents a power of 10; the kickoff decimal place being x¹, the 2d x², the third 10^three, and so on. Simply determine what ability of 10 the decimal extends to, employ that ability of 10 as the denominator, enter each number to the right of the decimal point equally the numerator, and simplify. For case, looking at the number 0.1234, the number 4 is in the 4th decimal place, which constitutes x^four, or 10,000. This would make the fraction

, which simplifies to

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

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

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

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

Common 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.

64th	32nd	16thursday	8thursday	4th	twond	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
ii/64	one/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	2/32	ane/sixteen				0.0625	ane.5875
five/64						0.078125	1.984375
6/64	3/32					0.09375	2.38125
seven/64						0.109375	2.778125
8/64	4/32	2/16	one/eight			0.125	3.175
nine/64						0.140625	3.571875
10/64	v/32					0.15625	iii.96875
11/64						0.171875	4.365625
12/64	6/32	3/16				0.1875	4.7625
xiii/64						0.203125	5.159375
14/64	vii/32					0.21875	5.55625
xv/64						0.234375	five.953125
16/64	8/32	iv/16	ii/8	1/iv		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
19/64						0.296875	7.540625
20/64	ten/32	v/xvi				0.3125	7.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	8.73125
23/64						0.359375	ix.128125
24/64	12/32	vi/16	3/eight			0.375	9.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	14/32	vii/16				0.4375	11.1125
29/64						0.453125	xi.509375
thirty/64	15/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	8/sixteen	4/8	2/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	eighteen/32	9/16				0.5625	fourteen.2875
37/64						0.578125	xiv.684375
38/64	19/32					0.59375	xv.08125
39/64						0.609375	15.478125
40/64	20/32	10/sixteen	5/eight			0.625	fifteen.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	eighteen.653125
48/64	24/32	12/sixteen	6/8	3/4		0.75	19.05
49/64						0.765625	xix.446875
l/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
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	14/16	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	xxx/32	xv/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/xvi	viii/8	4/4	two/2	1	25.four