Two finger exercises for the fretting hand 2 of 4

Below are multiple fraction giaidap.infos capable of addition, subtraction, multiplication, division, simplification, & conversion between fractions và decimals. Fields above sầu the solid blachồng line represent the numerator, while fields below represent the denominator.

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+ - x / = ?
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Mixed Numbers giaidap.info

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Simplify Fractions giaidap.info

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Decimal lớn Fraction giaidap.info

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Fraction lớn Decimal giaidap.info

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Big Number Fraction giaidap.info

Use this giaidap.info if the numerators or denominators are 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 a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that ảo diệu said whole. For example, in the fraction of
3
8
, the numerator is 3, & the denominator is 8. A more illustrative sầu example could involve sầu a pie with 8 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 lớn eat 3 slices, the remaining fraction of the pie would therefore be
5
8
as shown in the image to lớn the right. chú ý that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlượt thích adding and subtracting integers such as 2 và 8, fractions require a comtháng denominator to lớn undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the sản phẩm 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 lớn be multiplied by the appropriate factors lớn preserve sầu the value of the fraction as a whole. This is arguably the simplest way lớn ensure that the fractions have a comtháng denominator. However, in most cases, the solutions to lớn these equations will not appear in simplified khung (the provided giaidap.info computes the simplification 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 process can be used for any number of fractions. Just multiply the numerators & denominators of each fraction in the problem by the hàng hóa of the denominators of all the other fractions (not including its own respective sầu denominator) in the problem.

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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 sầu method for finding a common denominator is lớn determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to lớn result in a fraction in simplified size. In the example above sầu, the denominators were 4, 6, và 2. The least comtháng multiple is the first shared multiple 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 first multiple they all giới thiệu 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 problem by whatever 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 subtraction is essentially the same as fraction addition. A comtháng denominator is required for the operation lớn occur. Refer khổng lồ the addition section as well as the equations 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. Unlượt thích adding và subtracting, it is not necessary to compute a common denominator in order khổng lồ multiply fractions. Simply, the numerators và denominators of each fraction are multiplied, & the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer lớn 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 that for multiplying fractions. In order to lớn 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
1
a
. When a is a fraction, this essentially involves exchanging the position of the numerator và the denominator. The reciprocal of the fraction
3
4
would therefore be
4
3
. Refer to lớn the equations 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 easier khổng lồ work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.
220
440
for example, is more cumbersome than
1
2
. The giaidap.info provided returns fraction inputs in both improper fraction form as well as mixed number khung. In both cases, fractions are presented in their lowest forms by dividing both numerator & denominator by their greakiểm tra common factor.

Converting between fractions and decimals:

Converting from decimals to lớn fractions is straightforward. It does, however, require the understanding that each decimal place khổng lồ the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, & so on. Simply determine what power of 10 the decimal extends to lớn, use that power of 10 as the denominator, enter each number to lớn the right of the decimal point as the numerator, & 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 make the fraction
1234
10000
, which simplifies to lớn
617
5000
, since the greademo comtháng factor between the numerator và denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted lớn powers of 10) can be translated to lớn decimal size using the same principles. Take the fraction
1
2
for example. To convert this fraction inkhổng lồ a decimal, first convert it into lớn the fraction of
5
10
. Knowing that the first decimal place represents 10-1,
5
10
can be converted lớn 0.5. If the fraction were instead
5
100
, the decimal would then be 0.05, và so on. Beyond this, converting fractions inlớn decimals requires the operation of long division.

Comtháng Engineering Fraction to lớn Decimal Conversions

In engineering, fractions are widely used khổng lồ describe the kích thước of components such as pipes & bolts. The most comtháng fractional & decimal equivalents are listed below.

64th32nd16th8th4th2ndDecimalDecimal(inch to lớn 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
51/640.796875đôi mươi.240625
52/6426/3213/160.8125trăng tròn.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


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