Abstract algebra

     

Below are multiple fraction khovattuhoanthien.coms capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions & decimals. Fields above the solid đen line represent the numerator, while fields below represent the denominator.

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Mixed Numbers khovattuhoanthien.com

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Simplify Fractions khovattuhoanthien.com

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Decimal to Fraction khovattuhoanthien.com

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Fraction to Decimal khovattuhoanthien.com

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Big Number Fraction khovattuhoanthien.com

Use this khovattuhoanthien.com 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 & a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that cosplay said whole. For example, in the fraction of

3
8
, the numerator is 3, & the denominator is 8. A more illustrative example could involve 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:

Unlike adding và subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators và 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 lớn be a multiple of each individual denominator. The numerators also need to lớn be multiplied by the appropriate factors lớn preserve the value of the fraction as a whole. This is arguably the simplest way khổng lồ ensure that the fractions have a common denominator. However, in most cases, the solutions khổng lồ these equations will not appear in simplified form (the provided khovattuhoanthien.com 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 và denominators of each fraction in the problem by the sản phẩm of the denominators of all the other fractions (not including its own respective 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 method for finding a common denominator is to lớn determine the least common multiple (LCM) for the denominators, then showroom or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, và 2. The least common 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 nội dung is 12, so this is the least common multiple. Khổng lồ complete an addition (or subtraction) problem, multiply the numerators và denominators of each fraction in the problem by whatever value will make the denominators 12, then địa chỉ 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 common denominator is required for the operation to occur. Refer to lớn 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. Unlike adding & subtracting, it is not necessary lớn compute a common denominator in order khổng lồ multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, và 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 lớn 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 simply

1
a
. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction
3
4
would therefore be
4
3
. Refer to 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 lớn 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 khovattuhoanthien.com provided returns fraction inputs in both improper fraction form as 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 & 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 nguồn of 10 the decimal extends to, use that power of 10 as the denominator, enter each number khổng lồ 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 make the fraction

1234
10000
, which simplifies to lớn
617
5000
, since the greatest common factor between the numerator & denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated lớn decimal size using the same principles. Take the fraction

1
2
for example. Khổng lồ convert this fraction into a decimal, first convert it into the fraction of
5
10
. Knowing that the first decimal place represents 10-1,
5
10
can be converted to lớn 0.5. If the fraction were instead
5
100
, the decimal would then be 0.05, & so on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction lớn Decimal Conversions

In engineering, fractions are widely used to lớn describe the size of components such as pipes & bolts. The most common fractional và decimal equivalents are listed below.

64th32nd16th8th4th2ndDecimalDecimal(inch khổng lồ 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