2 x 1/3

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

Mixed Numbers Calculator

Simplify Fractions Calculator

Decimal to tướng Fraction Calculator

Fraction to tướng Decimal Calculator

Big Number Fraction Calculator

Use this calculator if the numerators or denominators are very big integers.

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3 over 8

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 trang điểm said whole. For example, in the fraction of

, the numerator is 3, and 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 tướng eat 3 slices, the remaining fraction of the pie would therefore be

as shown in the image to tướng the right. Note 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 and subtracting integers such as 2 and 8, fractions require a common denominator to tướng undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to tướng be a multiple of each individual denominator. The numerators also need to tướng be multiplied by the appropriate factors to tướng preserve the value of the fraction as a whole. This is arguably the simplest way to tướng ensure that the fractions have a common denominator. However, in most cases, the solutions to tướng these equations will not appear in simplified khuông (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An alternative method for finding a common denominator is to tướng 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 tướng result in a fraction in simplified khuông. In the example above, the denominators were 4, 6, and 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 share is 12, so sánh 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.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to tướng occur. Refer to tướng the addition section as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to tướng compute a common denominator in order to tướng multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to tướng the equations below for clarification.

Division:

The process for dividing fractions is similar to tướng that for multiplying fractions. In order to tướng 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

. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction

Xem thêm: trong dao động điều hòa

would therefore be

. Refer to tướng the equations below for clarification.

Simplification:

It is often easier to tướng work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome phàn nàn

. The calculator provided returns fraction inputs in both improper fraction khuông as well as mixed number khuông. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to tướng fractions is straightforward. It does, however, require the understanding that each decimal place to tướng the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, and so sánh on. Simply determine what power of 10 the decimal extends to tướng, use that power of 10 as the denominator, enter each number to tướng 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

, which simplifies to tướng

, since the greatest common factor between the numerator and denominator is 2.

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

for example. To convert this fraction into a decimal, first convert it into the fraction of

. Knowing that the first decimal place represents 10-1,

Xem thêm: 1+2+3+...+100

can be converted to tướng 0.5. If the fraction were instead

, the decimal would then be 0.05, and so sánh on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction to tướng Decimal Conversions

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

64th32nd16th8th4th2ndDecimalDecimal
(inch to tướng mm)
1/64     0.0156250.396875
2/641/32    0.031250.79375
3/64     0.0468751.190625
4/642/321/16   0.06251.5875
5/64     0.0781251.984375
6/643/32    0.093752.38125
7/64     0.1093752.778125
8/644/322/161/8  0.1253.175
9/64     0.1406253.571875
10/645/32    0.156253.96875
11/64     0.1718754.365625
12/646/323/16   0.18754.7625
13/64     0.2031255.159375
14/647/32    0.218755.55625
15/64     0.2343755.953125
16/648/324/162/81/4 0.256.35
17/64     0.2656256.746875
18/649/32    0.281257.14375
19/64     0.2968757.540625
20/6410/325/16   0.31257.9375
21/64     0.3281258.334375
22/6411/32    0.343758.73125
23/64     0.3593759.128125
24/6412/326/163/8  0.3759.525
25/64     0.3906259.921875
26/6413/32    0.4062510.31875
27/64     0.42187510.715625
28/6414/327/16   0.437511.1125
29/64     0.45312511.509375
30/6415/32    0.4687511.90625
31/64     0.48437512.303125
32/6416/328/164/82/41/20.512.7
33/64     0.51562513.096875
34/6417/32    0.5312513.49375
35/64     0.54687513.890625
36/6418/329/16   0.562514.2875
37/64     0.57812514.684375
38/6419/32    0.5937515.08125
39/64     0.60937515.478125
40/6420/3210/165/8  0.62515.875
41/64     0.64062516.271875
42/6421/32    0.6562516.66875
43/64     0.67187517.065625
44/6422/3211/16   0.687517.4625
45/64     0.70312517.859375
46/6423/32    0.7187518.25625
47/64     0.73437518.653125
48/6424/3212/166/83/4 0.7519.05
49/64     0.76562519.446875
50/6425/32    0.7812519.84375
51/64     0.79687520.240625
52/6426/3213/16   0.812520.6375
53/64     0.82812521.034375
54/6427/32    0.8437521.43125
55/64     0.85937521.828125
56/6428/3214/167/8  0.87522.225
57/64     0.89062522.621875
58/6429/32    0.9062523.01875
59/64     0.92187523.415625
60/6430/3215/16   0.937523.8125
61/64     0.95312524.209375
62/6431/32    0.9687524.60625
63/64     0.98437525.003125
64/6432/3216/168/84/42/2125.4