Below are multiple fraction wgc2010.orgs capable of addition, subtraction, multiplication, division, simplification, and also conversion in between fractions and also decimals. Fields over the solid black line represent the numerator, while fields below represent the denominator.

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Mixed number wgc2010.org

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Simplify fractions wgc2010.org

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Decimal to portion wgc2010.org

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Fraction come Decimal wgc2010.org

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Big Number fraction wgc2010.org

Use this wgc2010.org if the numerators or denominators room very big integers.

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In mathematics, a fraction is a number the represents a part of a whole. It is composed of a numerator and also a denominator. The molecule represents the variety 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
3
8
, the numerator is 3, and the denominator is 8. A much more illustrative example can involve a pie with 8 slices. 1 of those 8 slices would certainly constitute the molecule of a fraction, while the complete of 8 slices that comprises the whole pie would certainly be the denominator. If a person were come eat 3 slices, the remaining fraction of the pie would because of this be
5
8
as displayed in the picture to the right. Note that the denominator the a fraction cannot be 0, as it would make the fraction undefined. Fractions deserve to undergo countless different operations, few of which are pointed out below.

Addition:

Unlike adding and individually integers such together 2 and 8, fractions call for a typical denominator come undergo this operations. One method for recognize a usual denominator entails multiplying the numerators and denominators of every one of the fractions associated by the product that the denominators of every fraction. Multiplying all of the platform ensures the the new denominator is certain to be a multiple of every individual denominator. The numerators additionally need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is maybe the simplest means to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will certainly not appear in simplified type (the listed wgc2010.org computes the simplification automatically). Listed below is an instance using this method.

a
b
+ c
d
= a×d
b×d
+ c×b
d×b
= ad + bc
bd
EX: 3
4
+ 1
6
= 3×6
4×6
+ 1×4
6×4
= 22
24
= 11
12

This process can be used for any number of fractions. Just multiply the numerators and also denominators the each fraction in the trouble by the product the the platform of every the other fractions (not consisting of its very own respective denominator) in the problem.

EX: 1
4
+ 1
6
+ 1
2
= 1×6×2
4×6×2
+ 1×4×2
6×4×2
+ 1×4×6
2×4×6
=12
48
+ 8
48
+ 24
48
= 44
48
= 11
12

An alternative method for detect a typical denominator is to identify the least usual multiple (LCM) for the denominators, then add or subtract the numerators together one would an integer. Using the least usual multiple deserve to be an ext efficient and is an ext likely to result in a portion in streamlined form. In the instance above, the denominators were 4, 6, and also 2. The least usual multiple is the very first shared multiple of these three numbers.

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

The an initial multiple they every share is 12, for this reason this is the least usual multiple. To finish an enhancement (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by every little thing value will make the platform 12, then include the numerators.

EX: 1
4
+ 1
6
+ 1
2
= 1×3
4×3
+ 1×2
6×2
+ 1×6
2×6
=3
12
+ 2
12
+ 6
12
= 11
12

Subtraction:

Fraction individually is basically the same as portion addition. A common denominator is required for the operation to occur. Refer to the addition section and also the equations listed below for clarification.

See more: " You Are Doing That Too Much. Try Again In 8 Minutes., You Are Doing That Too Much

a
b
– c
d
= a×d
b×d
– c×b
d×b
= ad – bc
bd
EX: 3
4
– 1
6
= 3×6
4×6
– 1×4
6×4
= 14
24
= 7
12

Multiplication:

Multiplying fractions is relatively straightforward. Unlike including and subtracting, it is not crucial to compute a common denominator in order to multiply fractions. Simply, the numerators and also denominators the each fraction are multiplied, and also the an outcome forms a brand-new numerator and denominator. If possible, the solution need to be simplified. Describe the equations below for clarification.

a
b
× c
d
= ac
bd
EX: 3
4
× 1
6
= 3
24
= 1
8

Division:

The procedure for dividing fractions is similar to the for multiply fractions. In bespeak to divide fractions, the portion in the molecule is multiply by the mutual of the portion in the denominator. The mutual of a number a is simply
1
a
. As soon as a is a fraction, this essentially entails exchanging the position of the numerator and also the denominator. The mutual of the portion
3
4
would because of this be
4
3
. Describe the equations listed below for clarification.

a
b
/ c
d
= a
b
× d
c
= ad
bc
EX: 3
4
/ 1
6
= 3
4
× 6
1
= 18
4
= 9
2

Simplification:

It is often simpler to job-related with streamlined fractions. Together such, portion solutions are typically expressed in their streamlined forms.
220
440
because that example, is more cumbersome than
1
2
. The wgc2010.org listed returns fraction inputs in both not correct fraction kind as fine as blended number form. In both cases, fractions are presented in their lowest forms by separating both numerator and also denominator by your greatest typical factor.

Converting in between fractions and decimals:

Converting from decimal to fractions is straightforward. That does, however, require the expertise that every decimal ar to the best of the decimal suggest represents a strength of 10; the an initial decimal place being 101, the 2nd 102, the third 103, and also so on. Simply determine what strength of 10 the decimal expand to, usage that strength of 10 together the denominator, enter each number come the right of the decimal point as 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 10,000. This would certainly make the portion
1234
10000
, i beg your pardon simplifies to
617
5000
, because the greatest common factor between the numerator and also denominator is 2.

Similarly, fractions v denominators that room powers the 10 (or deserve to be converted to strength of 10) can be interpreted to decimal form using the very same principles. Take it the portion
1
2
for example. To transform this portion into a decimal, very first convert it into the portion of
5
10
. Learning that the very first decimal ar represents 10-1,
5
10
have the right to be converted to 0.5. If the portion were instead
5
100
, the decimal would then be 0.05, and also so on. Beyond this, convert fractions into decimals requires the operation of lengthy division.

Common Engineering portion to Decimal Conversions

In engineering, fractions room widely used to describe the dimension of contents such as pipes and also bolts. The most common fractional and also decimal equivalents are listed below.

64th32nd16th8th4th2ndDecimalDecimal(inch to mm)
1/640.0156250.396875
2/641/320.031250.79375
3/640.0468751.190625
4/642/321/160.06251.5875
5/640.0781251.984375
6/643/320.093752.38125
7/640.1093752.778125
8/644/322/161/80.1253.175
9/640.1406253.571875
10/645/320.156253.96875
11/640.1718754.365625
12/646/323/160.18754.7625
13/640.2031255.159375
14/647/320.218755.55625
15/640.2343755.953125
16/648/324/162/81/40.256.35
17/640.2656256.746875
18/649/320.281257.14375
19/640.2968757.540625
20/6410/325/160.31257.9375
21/640.3281258.334375
22/6411/320.343758.73125
23/640.3593759.128125
24/6412/326/163/80.3759.525
25/640.3906259.921875
26/6413/320.4062510.31875
27/640.42187510.715625
28/6414/327/160.437511.1125
29/640.45312511.509375
30/6415/320.4687511.90625
31/640.48437512.303125
32/6416/328/164/82/41/20.512.7
33/640.51562513.096875
34/6417/320.5312513.49375
35/640.54687513.890625
36/6418/329/160.562514.2875
37/640.57812514.684375
38/6419/320.5937515.08125
39/640.60937515.478125
40/6420/3210/165/80.62515.875
41/640.64062516.271875
42/6421/320.6562516.66875
43/640.67187517.065625
44/6422/3211/160.687517.4625
45/640.70312517.859375
46/6423/320.7187518.25625
47/640.73437518.653125
48/6424/3212/166/83/40.7519.05
49/640.76562519.446875
50/6425/320.7812519.84375
51/640.79687520.240625
52/6426/3213/160.812520.6375
53/640.82812521.034375
54/6427/320.8437521.43125
55/640.85937521.828125
56/6428/3214/167/80.87522.225
57/640.89062522.621875
58/6429/320.9062523.01875
59/640.92187523.415625
60/6430/3215/160.937523.8125
61/640.95312524.209375
62/6431/320.9687524.60625
63/640.98437525.003125
64/6432/3216/168/84/42/2125.4