Below space multiple portion betterworld2016.orgs capable of addition, subtraction, multiplication, division, simplification, and also conversion in between fractions and decimals. Fields over the solid black line represent the numerator, when fields listed below represent the denominator.

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Mixed numbers betterworld2016.org

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Simplify fractions betterworld2016.org

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Decimal to portion betterworld2016.org

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Fraction come Decimal betterworld2016.org

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Big Number portion betterworld2016.org

Use this betterworld2016.org if the molecule or denominators room very large integers.

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In mathematics, a fraction is a number the represents a component of a whole. It is composed of a numerator and also a denominator. The molecule represents the variety of equal components of a whole, when the denominator is the total number of parts that consist of said whole. Because that example, in the portion of
3
8
, the molecule is 3, and the denominator is 8. A more illustrative example might involve a pie with 8 slices. 1 of those 8 slices would certainly constitute the molecule of a fraction, when the total of 8 slices the comprises the entirety 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 shown in the picture to the right. Note that the denominator that a fraction cannot be 0, together it would make the portion undefined. Fractions deserve to undergo countless different operations, several of which are discussed below.

Addition:

Unlike including and individually integers such as 2 and 8, fractions need a typical denominator come undergo these operations. One method for recognize a typical denominator entails multiplying the numerators and also denominators of all of the fractions connected by the product of the platform of every fraction. Multiplying every one of the platform ensures that the brand-new denominator is certain to be a many of every individual denominator. The numerators also need come be multiply by the ideal factors to maintain the value of the fraction as a whole. This is maybe the simplest method to ensure that the fractions have actually a usual denominator. However, in many cases, the solutions to this equations will certainly not show up in simplified type (the noted betterworld2016.org computes the leveling automatically). Below is an example 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 procedure can be used for any number of fractions. Just multiply the numerators and also denominators the each fraction in the difficulty by the product the the denominators of all the other fractions (not consisting of its 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 technique for detect a typical denominator is to identify the least typical multiple (LCM) for the denominators, then add or subtract the numerators together one would an integer. Using the least typical multiple deserve to be more efficient and is more likely to result in a portion in simplified form. In the instance above, the denominators were 4, 6, and 2. The least common multiple is the first shared many of these three numbers.

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

The very first multiple they all share is 12, therefore this is the least typical multiple. To finish an enhancement (or subtraction) problem, multiply the numerators and denominators the each fraction in the difficulty by every little thing value will certainly make the platform 12, then add 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 essentially the same as portion addition. A common denominator is required for the operation to occur. Describe the enhancement section and also the equations listed below for clarification.

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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 fountain is fairly straightforward. Unlike including and subtracting, it is not important to compute a common denominator in bespeak to main point fractions. Simply, the numerators and also denominators the each portion are multiplied, and the an outcome forms a brand-new numerator and denominator. If possible, the solution should 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 comparable to the for multiply fractions. In bespeak to division fractions, the portion in the molecule is multiplied by the reciprocal of the portion in the denominator. The mutual of a number a is just
1
a
. As soon as a is a fraction, this essentially requires exchanging the position of the numerator and the denominator. The mutual of the fraction
3
4
would thus be
4
3
. Refer to 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 much easier to work-related with simplified fractions. As such, portion solutions are commonly expressed in their simplified forms.
220
440
for example, is more cumbersome 보다
1
2
. The betterworld2016.org detailed returns portion inputs in both not correct fraction type as well as combined number form. In both cases, fractions space presented in their lowest develops by separating both numerator and denominator by their greatest usual factor.

Converting between fractions and also decimals:

Converting from decimals to fountain is straightforward. It does, however, need the expertise that each decimal ar to the appropriate of the decimal point represents a power of 10; the first decimal ar being 101, the second 102, the third 103, and also so on. Simply recognize what power of 10 the decimal extends to, use that power of 10 together the denominator, get in each number to the best of the decimal point as the numerator, and also simplify. For example, looking in ~ the number 0.1234, the number 4 is in the 4th decimal place, which constitutes 104, or 10,000. This would make the portion
1234
10000
, i beg your pardon simplifies come
617
5000
, because the greatest typical factor between the numerator and also denominator is 2.

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

Common Engineering portion to Decimal Conversions

In engineering, fractions room widely supplied to define the size of components such together pipes and also bolts. The most usual fractional and decimal equivalents are detailed below.

64th32nd16th8th4th2ndDecimalDecimal(inch come 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