Below are multiple fraction glaskragujevca.nets capable of addition, subtraction, multiplication, division, simplification, & conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.
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Mixed Numbers glaskragujevca.net
Simplify Fractions glaskragujevca.net
Decimal lớn Fraction glaskragujevca.net
Fraction lớn Decimal glaskragujevca.net
Big Number Fraction glaskragujevca.net
Use this glaskragujevca.net 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 and 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
, 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 eat 3 slices, the remaining fraction of the pie would therefore be
as shown in the image khổng lồ 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.
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 & 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 khổng lồ be multiplied by the appropriate factors to lớn 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 size (the provided glaskragujevca.net 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 sản phẩm of the denominators of all the other fractions (not including its own respective denominator) in the problem.
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|=|| + || + || = || = |
An alternative method for finding a common denominator is khổng lồ 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 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 share is 12, so this is the least common multiple. To 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 địa chỉ the numerators.
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|=|| + || + || = |
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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| – || = || – || = || – || = || – || = || = |
Multiplying fractions is fairly straightforward. Unlike adding và subtracting, it is not necessary khổng lồ compute a common denominator in order to lớn 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 to lớn the equations below for clarification.
| × || = || × || = || = |
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 . When a is a fraction, this essentially involves exchanging the position of the numerator & the denominator. The reciprocal of the fraction would therefore be . Refer khổng lồ the equations below for clarification.
| / || = || × || = || / || = || × || = || = |
It is often easier to lớn work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms. for example, is more cumbersome than . The glaskragujevca.net 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 and decimals:
Converting from decimals khổng lồ fractions is straightforward. It does, however, require the understanding that each decimal place to lớn the right of the decimal point represents a power nguồn of 10; the first decimal place being 101, the second 102, the third 103, và so on. Simply determine what nguồn of 10 the decimal extends to, use that power 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 , which simplifies to lớn , since the greatest common factor between the numerator and denominator is 2.
Similarly, fractions with denominators that are powers of 10 (or can be converted lớn powers of 10) can be translated to lớn decimal form using the same principles. Take the fraction for example. Khổng lồ convert this fraction into a decimal, first convert it into the fraction of . Knowing that the first decimal place represents 10-1, can be converted to 0.5. If the fraction were instead , 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 to Decimal Conversions
In engineering, fractions are widely used lớn describe the kích cỡ of components such as pipes & bolts. The most common fractional and decimal equivalents are listed below.
|64th||32nd||16th||8th||4th||2nd||Decimal||Decimal(inch to mm)|