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For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator. [2] As another example, if a×b=a×c, then the multiplicative term a can be canceled out if a≠0, resulting in the equivalent expression b=c; this is equivalent to dividing through by a.
In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...
Terms are within the same expression and are combined by either addition or subtraction. For example, take the expression: + There are two terms in this expression. Notice that the two terms have a common factor, that is, both terms have an . This means that the common factor variable can be factored out, resulting in
The quotient and remainder can then be determined as follows: Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of x, which in this case is x). Place the result above the bar (x 3 ÷ x = x 2).
If two numbers (whose average is a number which is easily squared) are multiplied, the difference of two squares can be used to give you the product of the original two numbers. For example: 27 × 33 = ( 30 − 3 ) ( 30 + 3 ) {\displaystyle 27\times 33=(30-3)(30+3)}
A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor. It can be fully reduced to lowest terms if both are divided by their greatest common divisor. [5] In order to find the greatest common divisor, the Euclidean algorithm or prime factorization can be used. The Euclidean algorithm is ...
Animation showing the use of synthetic division to find the quotient of + + + by .Note that there is no term in , so the fourth column from the right contains a zero.. In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
We can reduce the fractions to lowest terms by noting that the two occurrences of b on the left-hand side cancel, as do the two occurrences of d on the right-hand side, leaving =, and we can divide both sides of the equation by any of the elements—in this case we will use d —getting =.