9 16 1 2 Simplified

Fraction Calculator

Beneath are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

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Mixed Numbers Estimator

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Simplify Fractions Computer

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Decimal to Fraction Figurer

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Calculation steps:

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Fraction to Decimal Reckoner

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Big Number Fraction Reckoner

Use this calculator if the numerators or denominators are very large 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 upward said whole. For case, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. one of those viii slices would constitute the numerator of a fraction, while the total of viii slices that comprises the whole pie would be the denominator. If a person were to eat iii 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, equally information technology would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned beneath.

Improver:

Unlike adding and subtracting integers such as 2 and viii, 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 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 need to exist multiplied by the appropriate factors to preserve the value of the fraction every bit a whole. This is arguably the simplest fashion to ensure that the fractions accept a common denominator. However, in most cases, the solutions to these equations will not announced in simplified class (the provided estimator computes the simplification automatically). Below is an instance using this method.

This process tin be used for whatever 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 respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the to the lowest degree common multiple (LCM) for the denominators, then add together or subtract the numerators as one would an integer. Using the to the lowest degree common multiple can be more efficient and is more likely to effect in a fraction in simplified form. In the example to a higher place, the denominators were 4, vi, and ii. The least common multiple is the first shared multiple of these three numbers.

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

Multiples of 4: 4, 8, 12

Multiples of 6: half dozen, 12

The first multiple they all share is 12, then this is the least mutual multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the trouble past whatever value volition brand the denominators 12, so 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 too as the equations beneath for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in club to multiply fractions. Simply, 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 below for clarification.

Segmentation:

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 merely

. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction

would therefore exist

. Refer to the equations below for clarification.

Simplification:

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

for example, is more cumbersome than

. The reckoner provided returns fraction inputs in both improper fraction form equally well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common 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 correct of the decimal point represents a power of 10; the first decimal place being 10¹, the 2d 10ⁱⁱ, the tertiary 10³, and so on. Simply determine what power of ten the decimal extends to, apply that ability of 10 every bit the denominator, enter each number to the right of the decimal bespeak every bit the numerator, and simplify. For example, looking at the number 0.1234, the number iv 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 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 class 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 first decimal identify represents 10^-1,

can be 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 science Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most mutual 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	1/32					0.03125	0.79375
3/64						0.046875	ane.190625
4/64	2/32	1/16				0.0625	one.5875
5/64						0.078125	1.984375
6/64	3/32					0.09375	2.38125
seven/64						0.109375	2.778125
viii/64	4/32	2/16	1/eight			0.125	three.175
nine/64						0.140625	iii.571875
10/64	5/32					0.15625	3.96875
11/64						0.171875	4.365625
12/64	6/32	3/sixteen				0.1875	4.7625
thirteen/64						0.203125	5.159375
14/64	7/32					0.21875	v.55625
fifteen/64						0.234375	5.953125
16/64	eight/32	4/16	2/viii	1/4		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
xix/64						0.296875	vii.540625
20/64	10/32	5/sixteen				0.3125	7.9375
21/64						0.328125	viii.334375
22/64	eleven/32					0.34375	viii.73125
23/64						0.359375	9.128125
24/64	12/32	6/16	3/8			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	7/16				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	16/32	viii/16	4/8	2/4	1/2	0.5	12.7
33/64						0.515625	xiii.096875
34/64	17/32					0.53125	13.49375
35/64						0.546875	13.890625
36/64	18/32	9/sixteen				0.5625	14.2875
37/64						0.578125	xiv.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	15.478125
40/64	xx/32	10/16	v/8			0.625	fifteen.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	11/16				0.6875	17.4625
45/64						0.703125	17.859375
46/64	23/32					0.71875	eighteen.25625
47/64						0.734375	18.653125
48/64	24/32	12/xvi	6/viii	three/four		0.75	xix.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	xix.84375
51/64						0.796875	xx.240625
52/64	26/32	13/16				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	seven/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	thirty/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/16	8/8	iv/four	ii/two	1	25.4