Home / Tổng hợp / find 1/2, 1/4, 1/3 or 3/4 of a set of objects differentiated
FIND 1/2, 1/4, 1/3 OR 3/4 OF A SET OF OBJECTS DIFFERENTIATED
admin -
24/12/2022 16
Below are multiple fraction thuphikhongdung.vns capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.
Use this thuphikhongdung.vn 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 trang điểm 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 to lớn eat 3 slices, the remaining fraction of the pie would therefore be
5
8
as shown in the image 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 lớn undergo these operations. One method for finding a common denominator involves multiplying the numerators & 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 to be a multiple of each individual denominator. The numerators also need lớn be multiplied by the appropriate factors khổng lồ preserve the value of the fraction as a whole. This is arguably the simplest way lớn ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided thuphikhongdung.vn computes the simplification automatically). Below is an example using this method.
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, 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 cốt truyện is 12, so this is the least common multiple. Khổng lồ complete an addition (or subtraction) problem, multiply the numerators & denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.
Multiplying fractions is fairly straightforward. Unlike adding & subtracting, it is not necessary khổng lồ compute a common denominator in order khổng lồ multiply fractions. Simply, the numerators & denominators of each fraction are multiplied, & the result forms a new numerator và 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 to 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 & the denominator. The reciprocal of the fraction
3
4
would therefore be
4
3
. Refer 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 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 thuphikhongdung.vn 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 và 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 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 power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to 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 lớn powers of 10) can be translated lớn decimal form 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 lớn 0.5. If the fraction were instead
5
100
, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.
Common Engineering Fraction to Decimal Conversions
In engineering, fractions are widely used lớn describe the kích cỡ of components such as pipes & bolts. The most common fractional & decimal equivalents are listed below.
