Below are multiple fraction chudongthanghoa.coms capable of addition, subtraction, multiplication, division, simplification, và conversion between fractions & decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.
Use this chudongthanghoa.com if the numerators or denominators are very big integers.
+ - x /
= ?
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 biến hóa 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 khổng lồ the right. lưu 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 and subtracting integers such as 2 and 8, fractions require a comtháng denominator to lớn undergo these operations. One method for finding a common denominator involves multiplying the numerators & 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 khổng lồ be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors lớn preserve sầu the value of the fraction as a whole. This is arguably the simplest way khổng lồ ensure that the fractions have sầu a common denominator. However, in most cases, the solutions to these equations will not appear in simplified khung (the provided chudongthanghoa.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 product of the denominators of all the other fractions (not including its own respective sầu 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 sầu method for finding a common denominator is to lớn determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least comtháng multiple can be more efficient và is more likely lớn result in a fraction in simplified size. In the example above sầu, the denominators were 4, 6, & 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 comtháng multiple. To 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 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 to lớn occur. Refer lớn the addition section as well as the equations below for clarification.
Multiplying fractions is fairly straightforward. Unlike adding và subtracting, it is not necessary khổng lồ compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, và the result forms a new numerator & 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 khổng lồ 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 và 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 to 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 chudongthanghoa.com provided returns fraction inputs in both improper fraction size as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator và denominator by their greakiểm tra common factor.
Converting between fractions và decimals:
Converting from decimals lớn fractions is straightforward. It does, however, require the understanding that each decimal place lớn 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 on. Simply determine what power of 10 the decimal extends 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 khổng lồ
617
5000
, since the greademo comtháng factor between the numerator and 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 khung using the same principles. Take the fraction
1
2
for example. To 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 khổng lồ 0.5. If the fraction were instead
5
100
, the decimal would then be 0.05, và so on. Beyond this, converting fractions into decimals requires the operation of long division.
Comtháng Engineering Fraction to Decimal Conversions
In engineering, fractions are widely used lớn describe the form size of components such as pipes và bolts. The most common fractional & decimal equivalents are listed below.
