It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms. 220 An 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. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers. Multiples of 2: 2, 4, 6, 8 10, 12 Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification. a 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 10 1, the second 10 2, the third 10 3, and so on. 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. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10 4, or 10,000. This would make the fraction 1234 A polynomial with rational coefficients can sometimes be written as a product of lower-degree polynomials that also have rational coefficients. In such cases, the polynomial is said to "factor over the rationals." Factoring is a useful way to find rational roots (which correspond to linear factors) and simple roots involving square roots of integers (which correspond to quadratic factors).

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. EX: When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction 3 as shown in the image to the right. Note 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. In mathematical context, it is a handy practice to arrange the given data in a sorted way before you apply various operations to obtain the results. First, start from the most left and compare the first single digit in both numbers which is 2 as shown below:In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below. 64 th the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division. Intel classifications are for general, educational and planning purposes only and consist of Export Control Classification Numbers (ECCN) and Harmonized Tariff Schedule (HTS) numbers. Any use made of Intel classifications are without recourse to Intel and shall not be construed as a representation or warranty regarding the proper ECCN or HTS. Your company as an importer and/or exporter is responsible for determining the correct classification of your transaction. Unlike adding and 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 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 to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method. a

Wolfram|Alpha is a great tool for factoring, expanding or simplifying polynomials. It also multiplies, divides and finds the greatest common divisors of pairs of polynomials; determines values of polynomial roots; plots polynomials; finds partial fraction decompositions; and more. 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. Take the fraction 1the 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 5 Polynomials with rational coefficients always have as many roots, in the complex plane, as their degree; however, these roots are often not rational numbers. In such cases, the polynomial will not factor into linear polynomials. When multiplying decimals, say, 0.2 0.2 0.2 and 1.25 1.25 1.25, we can begin by forgetting the dots. That means that to find 0.2 × 1.25 0.2 \times 1.25 0.2 × 1.25, we start by finding 2 × 125 2 \times 125 2 × 125, which is 250 250 250. Then we count how many digits to the right of the dots we had in total in the numbers we started with (in this case, it's three: one in 0.2 0.2 0.2 and two in 1.25 1.25 1.25). We then write the dot that many digits from the right in what we obtained. For us, this translates to putting the dot to the left of 2 2 2, which gives 0.250 = 0.25 0.250 = 0.25 0.250 = 0.25 (we write 0 0 0 if we have no number in front of the dot).