Below are multiple fraction mctq.vns capable of addition, subtraction, multiplication, division, simplification, và conversion between fractions & decimals. Fields above the solid blaông xã line represent the numerator, while fields below represent the denominator.
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Mixed Numbers mctq.vn
Simplify Fractions mctq.vn
Decimal to lớn Fraction mctq.vn
Fraction to Decimal mctq.vn
Big Number Fraction mctq.vn
Use this mctq.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 Cosplay said whole. For example, in the fraction of
, the numerator is 3, và the denominator is 8. A more illustrative sầu 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 khổng lồ eat 3 slices, the remaining fraction of the pie would therefore be
as shown in the image lớn the right. chú 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.
Unlượt thích adding and subtracting integers such as 2 & 8, fractions require a comtháng denominator to 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 lớn be a multiple of each individual denominator. The numerators also need khổng lồ 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 mctq.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 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 sầu method for finding a comtháng denominator is to 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 khổng lồ result in a fraction in simplified form. In the example above sầu, the denominators were 4, 6, & 2. The least comtháng 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. To 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.
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|=|| + || + || = |
Fraction subtraction is essentially the same as fraction addition. A comtháng denominator is required for the operation lớn occur. Refer lớn the addition section as well as the equations below for clarification.
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| – || = || – || = || – || = || – || = || = |
Multiplying fractions is fairly straightforward. Unlike adding & subtracting, it is not necessary to compute a comtháng denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator và denominator. If possible, the solution should be simplified. Refer khổng lồ the equations below for clarification.
| × || = || × || = || = |
The process for dividing fractions is similar to lớn 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 and the denominator. The reciprocal of the fraction would therefore be . Refer to the equations below for clarification.
| / || = || × || = || / || = || × || = || = |
It is often easier lớn work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms. for example, is more cumbersome than . The mctq.vn provided returns fraction inputs in both improper fraction khung as well as mixed number size. In both cases, fractions are presented in their lowest forms by dividing both numerator & denominator by their greathử nghiệm common factor.
Converting between fractions and decimals:
Converting from decimals lớn fractions is straightforward. It does, however, require the understanding that each decimal place lớn 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 lớn, use that power of 10 as the denominator, enter each number 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 , which simplifies to , since the greakiểm tra 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 khung using the same principles. Take the fraction for example. To convert this fraction into lớn a decimal, first convert it into the fraction of . Knowing that the first decimal place represents 10-1, can be converted to lớn 0.5. If the fraction were instead , 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 lớn Decimal Conversions
In engineering, fractions are widely used lớn describe the kích cỡ of components such as pipes & bolts. The most comtháng fractional and decimal equivalents are listed below.
|64th||32nd||16th||8th||4th||2nd||Decimal||Decimal(inch to lớn mm)|