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

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Mixed number occupychristmas.org

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Simplify fractions occupychristmas.org

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Decimal to fraction occupychristmas.org

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Fraction come Decimal occupychristmas.org

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Big Number fraction occupychristmas.org

Use this occupychristmas.org if the molecule or denominators room very big 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 also a denominator. The molecule represents the number of equal components of a whole, if the denominator is the total variety of parts that consist of said whole. For example, in the fraction of
3
8
, the numerator is 3, and also the denominator is 8. A more illustrative example could involve a pie through 8 slices. 1 the those 8 slices would constitute the molecule of a fraction, when the total of 8 slices the comprises the whole pie would certainly be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would as such be
5
8
as presented in the photo to the right. Keep in mind that the denominator the a fraction cannot be 0, together it would make the portion undefined. Fractions can undergo numerous different operations, some of which are mentioned below.

Addition:

Unlike adding and individually integers such together 2 and also 8, fractions require a usual denominator come undergo these operations. One technique for recognize a usual denominator entails multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying every one of the denominators ensures that the new denominator is particular to be a multiple of every individual denominator. The numerators likewise need to be multiplied by the suitable factors to keep the value of the fraction as a whole. This is maybe the simplest means to ensure that the fractions have a usual denominator. However, in most cases, the services to this equations will certainly not show up in simplified form (the detailed occupychristmas.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 variety of fractions. Simply multiply the numerators and denominators the each fraction in the trouble by the product the the platform of all the various other fractions (not including 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 technique for finding a typical denominator is to identify the least typical multiple (LCM) because that the denominators, then add or subtract the numerators as one would an integer. Using the least typical multiple have the right to be much more efficient and also is more likely to an outcome in a fraction in streamlined form. In the example above, the denominators were 4, 6, and also 2. The least typical multiple is the an initial shared multiple of these 3 numbers.

Multiples that 2: 2, 4, 6, 8 10, 12
Multiples the 4: 4, 8, 12
Multiples that 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 difficulty by everything value will make the denominators 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 basically the exact same as fraction addition. A typical denominator is forced for the operation to occur. Describe the addition 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 fractions is fairly straightforward. Unlike adding and subtracting, that is not crucial to compute a common denominator in stimulate to multiply fractions. Simply, the numerators and denominators the each portion are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

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

Division:

The process for dividing fractions is similar to the for multiply fractions. In stimulate to division fractions, the portion in the molecule is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is merely
1
a
. When a is a fraction, this essentially requires exchanging the place of the numerator and the denominator. The reciprocal of the portion
3
4
would because of this 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 simpler to occupational with simplified fractions. As such, portion solutions are commonly expressed in their streamlined forms.
220
440
for example, is much more cumbersome than
1
2
. The occupychristmas.org detailed returns portion inputs in both wrong fraction type as fine as blended number form. In both cases, fractions are presented in their lowest creates by separating both numerator and denominator by their greatest common factor.

Converting in between fractions and decimals:

Converting from decimals to fractions is straightforward. That does, however, need the expertise that every decimal place to the right of the decimal allude represents a power of 10; the an initial decimal location being 101, the 2nd 102, the third 103, and so on. Simply identify what strength of 10 the decimal expand to, use that strength of 10 as the denominator, go into each number to the appropriate of the decimal allude as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, i beg your pardon constitutes 104, or 10,000. This would make the fraction
1234
10000
, which simplifies come
617
5000
, since the greatest usual factor between the numerator and denominator is 2.

Similarly, fractions v denominators that room powers of 10 (or deserve to be converted to powers of 10) can be translated to decimal type using the same principles. Take the fraction
1
2
because that example. To convert this portion into a decimal, an initial convert it into the fraction of
5
10
. Discovering that the very first decimal location represents 10-1,
5
10
have the right to be convert to 0.5. If the portion were rather
5
100
, the decimal would certainly then be 0.05, and also so on. Beyond this, convert fractions into decimals calls for the operation of long division.

Common Engineering fraction to Decimal Conversions

In engineering, fractions space widely supplied to explain the dimension of contents such as pipes and also bolts. The most common fractional and also decimal equivalents are detailed 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