Below are multiple fraction temperocars.coms capable of addition, subtraction, multiplication, division, simplification, và conversion between fractions and decimals. Fields above the solid đen line represent the numerator, while fields below represent the denominator.
Use this temperocars.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 hóa trang said whole. For example, in the fraction of
3
8
, 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 khổng lồ eat 3 slices, the remaining fraction of the pie would therefore be
5
8
as shown in the image to lớn 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 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 product 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 khổng lồ 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 to lớn these equations will not appear in simplified size (the provided temperocars.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 & 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.
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 khổng lồ determine the least common multiple (LCM) for the denominators, then địa chỉ cửa hàng or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely lớn result in a fraction in simplified form. In the example above, 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 cốt truyện 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 showroom 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 khổng lồ the addition section as well as the equations below for clarification.
Multiplying fractions is fairly straightforward. Unlike adding & subtracting, it is not necessary lớn compute a common denominator in order to lớn multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, và the result forms a new numerator và 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 lớn that for multiplying fractions. In order 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 temperocars.com provided returns fraction inputs in both improper fraction khung as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator & denominator by their greatest 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 to lớn the right of the decimal point represents a nguồn of 10; the first decimal place being 101, the second 102, the third 103, và so on. Simply determine what power 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, và 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 lớn powers of 10) can be translated khổng lồ decimal khung using the same principles. Take the fraction
1
2
for example. To lớn 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 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 khổng lồ Decimal Conversions
In engineering, fractions are widely used lớn describe the form size of components such as pipes và bolts. The most common fractional và decimal equivalents are listed below.
