7 14 In Simplest Form

Fraction Calculator

Below are multiple fraction calculators capable of improver, subtraction, multiplication, division, simplification, and conversion betwixt fractions and decimals. Fields in a higher place the solid black line represent the numerator, while fields beneath 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 Figurer

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Fraction to Decimal Calculator

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Big Number Fraction Calculator

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 function 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 up said whole. For example, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with viii slices. 1 of those 8 slices would constitute 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 consume 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 be 0, as it would make the fraction undefined. Fractions tin undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 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 by 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 also demand to be multiplied by the advisable factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. Nevertheless, in most cases, the solutions to these equations will non appear in simplified grade (the provided computer computes the simplification automatically). Beneath is an example using this method.

This process tin can exist used for whatever number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the production of the denominators of all the other fractions (non including its own respective denominator) in the problem.

An culling method for finding a mutual denominator is to determine the least mutual multiple (LCM) for the denominators, so add or subtract the numerators every bit one would an integer. Using the least common multiple tin be more efficient and is more likely to result in a fraction in simplified grade. In the example above, the denominators were 4, half dozen, and 2. The least mutual multiple is the first shared multiple of these 3 numbers.

Multiples of 2: 2, 4, half-dozen, 8 10, 12

Multiples of 4: iv, viii, 12

Multiples of 6: six, 12

The showtime multiple they all share is 12, and then this is the least common multiple. To complete an addition (or subtraction) trouble, 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 as well equally the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Different calculation and subtracting, information technology is not necessary to compute a mutual denominator in order to multiply fractions. But, the numerators and denominators of each fraction are multiplied, and the issue forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations beneath 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 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 frequently easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome than

. The figurer provided returns fraction inputs in both improper fraction form also 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, notwithstanding, crave the understanding that each decimal place to the right of the decimal point represents a ability of 10; the first decimal place existence ten^ane, the 2nd 10², the third 10^three, and and then on. Simply determine what power of 10 the decimal extends to, use that power of x every bit the denominator, enter each number to the right of the decimal betoken as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the 4th decimal identify, which constitutes 10⁴, or 10,000. This would make the fraction

, which simplifies to

, since the greatest mutual gene between the numerator and denominator is two.

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, start convert it into the fraction of

. Knowing that the showtime decimal place represents ten^-ane,

can be converted to 0.5. If the fraction were instead

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

Common Engineering Fraction to Decimal Conversions

In technology, 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.

64^th	32^nd	16^th	8^th	4^th	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	ane/32					0.03125	0.79375
3/64						0.046875	1.190625
iv/64	2/32	1/16				0.0625	ane.5875
five/64						0.078125	ane.984375
6/64	3/32					0.09375	two.38125
7/64						0.109375	2.778125
8/64	iv/32	ii/xvi	i/8			0.125	3.175
ix/64						0.140625	iii.571875
10/64	five/32					0.15625	iii.96875
xi/64						0.171875	4.365625
12/64	6/32	three/16				0.1875	4.7625
xiii/64						0.203125	5.159375
14/64	7/32					0.21875	5.55625
fifteen/64						0.234375	5.953125
xvi/64	8/32	4/16	2/8	1/4		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	10/32	5/16				0.3125	7.9375
21/64						0.328125	8.334375
22/64	eleven/32					0.34375	viii.73125
23/64						0.359375	nine.128125
24/64	12/32	6/16	three/8			0.375	ix.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	ten.31875
27/64						0.421875	10.715625
28/64	fourteen/32	7/xvi				0.4375	11.1125
29/64						0.453125	eleven.509375
30/64	15/32					0.46875	eleven.90625
31/64						0.484375	12.303125
32/64	xvi/32	eight/16	4/eight	ii/4	i/2	0.5	12.vii
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	xiv.684375
38/64	nineteen/32					0.59375	15.08125
39/64						0.609375	xv.478125
40/64	twenty/32	x/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/xvi				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	6/8	3/4		0.75	19.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	xix.84375
51/64						0.796875	20.240625
52/64	26/32	13/16				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/sixteen	seven/viii			0.875	22.225
57/64						0.890625	22.621875
58/64	29/32					0.90625	23.01875
59/64						0.921875	23.415625
sixty/64	30/32	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	16/16	viii/viii	4/4	two/two	1	25.4