Adding, subtracting and finding the least common multiple

Big Number Fraction magdalenarybarikova.com

Use this magdalenarybarikova.com 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 & a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that 3d said whole. For example, in the fraction of

3

8

, the numerator is 3, và 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 and 8, fractions require a common denominator khổng lồ 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 to be a multiple of each individual denominator. The numerators also need to 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 these equations will not appear in simplified size (the provided magdalenarybarikova.com 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 and 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.

An alternative method for finding a common denominator is to lớn 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 khổng lồ 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.

The first multiple they all share is 12, so this is the least common multiple. To lớn 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 địa chỉ cửa hàng the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common 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. Unlike adding & subtracting, it is not necessary to lớn compute a common denominator in order khổng lồ multiply fractions. Simply, the numerators và denominators of each fraction are multiplied, and the result forms a new numerator và denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Division:

The process for dividing fractions is similar khổng lồ that for multiplying fractions. In order to 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 & the denominator. The reciprocal of the fraction

3

4

would therefore be

4

3

. Refer to the equations below for clarification.

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 magdalenarybarikova.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 & denominator by their greatest common factor.

Converting between fractions & decimals:

Converting from decimals khổng lồ fractions is straightforward. It does, however, require the understanding that each decimal place to 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 of 10 the decimal extends to, use that nguồn 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

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 to 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 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 lớn Decimal Conversions

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