Below are multiple fraction randy-rhoads-online.coms capable of addition, subtraction, multiplication, division, simplification, & conversion between fractions và decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.
Use this randy-rhoads-online.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 và a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up 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 lớn eat 3 slices, the remaining fraction of the pie would therefore be
5
8
as shown in the image to 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 và 8, fractions require a common denominator khổng lồ undergo these operations. One method for finding a common denominator involves multiplying the numerators & denominators of all of the fractions involved by the hàng hóa 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 be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions lớn these equations will not appear in simplified form (the provided randy-rhoads-online.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.
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 & is more likely to 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 nói qua is 12, so this is the least common multiple. Lớn 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 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 khổng lồ 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 to compute a common denominator in order lớn multiply fractions. Simply, the numerators & denominators of each fraction are multiplied, & the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer khổng lồ 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 khổng lồ 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 & the denominator. The reciprocal of the fraction
3
4
would therefore be
4
3
. Refer khổng lồ 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 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 randy-rhoads-online.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 và decimals:
Converting from decimals lớn fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power nguồn 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, use that power nguồn of 10 as the denominator, enter each number to lớn 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 khổng lồ
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 khổng lồ powers of 10) can be translated khổng lồ decimal form 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 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.
Common Engineering Fraction khổng lồ Decimal Conversions
In engineering, fractions are widely used to describe the form size of components such as pipes và bolts. The most common fractional and decimal equivalents are listed below.
