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Big Number Fraction joy6.vn

Use this joy6.vn if the numerators or denominators are very big integers.

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 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 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 to the right. cảnh báo 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:

Unlượt thích adding and subtracting integers such as 2 & 8, fractions require a comtháng denominator khổng lồ undergo these operations. One method for finding a comtháng 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 khổng lồ be a multiple of each individual denominator. The numerators also need khổng lồ be multiplied by the appropriate factors lớn preserve sầu the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a comtháng denominator. However, in most cases, the solutions to these equations will not appear in simplified size (the provided joy6.vn 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 & denominators of each fraction in the problem by the hàng hóa of the denominators of all the other fractions (not including its own respective sầu denominator) in the problem.

An alternative sầu method for finding a common denominator is lớn determine the least comtháng 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 & is more likely lớn result in a fraction in simplified form. In the example above sầu, the denominators were 4, 6, & 2. The least common multiple is the first shared multiple of these three numbers.

The first multiple they all chia sẻ is 12, so this is the least common 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.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A comtháng denominator is required for the operation to lớn occur. Refer khổng lồ the addition section as well as the equations below for clarification.

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Multiplication:

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

Division:

The process for dividing fractions is similar lớn 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 lớn the equations below for clarification.

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 joy6.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 greachạy thử comtháng factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, và so on. Simply determine what power 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 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 to powers of 10) can be translated khổng lồ decimal size using the same principles. Take the fraction

1

2

for example. To convert this fraction into a decimal, first convert it inlớn 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, & so on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction lớn Decimal Conversions

In engineering, fractions are widely used khổng lồ describe the kích cỡ of components such as pipes và bolts. The most common fractional and decimal equivalents are listed below.