Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. , since the greatest common factor between the numerator and denominator is 2. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10 4, or 10,000. 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. 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 10 1, the second 10 2, the third 10 3, and so on. Converting between fractions and decimals:Ĭonverting from decimals to fractions is straightforward. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor. The calculator provided returns fraction inputs in both improper fraction form as well as mixed number form. As such, fraction solutions are commonly expressed in their simplified forms. It is often easier to work with simplified fractions. Refer to the equations below for clarification. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The process for dividing fractions is similar to that for multiplying fractions. If possible, the solution should be simplified. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Multiplying fractions is fairly straightforward.
Refer to the addition section as well as the equations below for clarification. A common denominator is required for the operation to occur. EX:įraction subtraction is essentially the same as fraction addition. To 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 add the numerators. The first multiple they all share is 12, so this is the least common multiple. The least common multiple is the first shared multiple of these three numbers. In the example above, the denominators were 4, 6, and 2. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form.
EX:Īn alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. 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. This process can be used for any number of fractions. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). This is arguably the simplest way to ensure that the fractions have a common denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. Fractions can undergo many different operations, some of which are mentioned below. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be 5Īs shown in the image to the right. 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. A more illustrative example could involve a pie with 8 slices. , the numerator is 3, and the denominator is 8. 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. It consists of a numerator and a denominator. In mathematics, a fraction is a number that represents a part of a whole. Use this calculator if the numerators or denominators are very big integers.
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