College Algebra (Abridged)

9. Cancellation law for division: = , provided ≠ 0 and ≠ 0 . Absolute values , or the magnitude of an integer, are another vital concept to know in algebra. It is defined as the distance between the integer and the zero value on the number line. Absolute values are denoted by the modulus symbol | | where can be any integer, negative or positive. If we have to calculate the absolute value of -5, then it will be denoted by |-5|and is equal to 5, showing that the distance from -5 to 0 is 5 units. Some of the properties of absolute values are: | | = � ≥ 0 ( − ) < 0 | | ≥ 0 | − | = | | | ∗ | = | | ∗ | | Scientific Notation Sometimes we make use of some power of 10 that makes it convenient to write a very large number; this means we are making use of scientific notation. For instance, suppose we have to write the number 687657.788. We can write it as 6.87657788 × 10 5 . 1.2 Inequalities The value of different numbers can be compared by their relative position on the number line. For instance, in the given number line below, is less than and is denoted by < , which means lies to the left of on the number line. We can also say > , that is is greater than and lies on the right side of the number line, relative to the position of . The mathematical representation for different expressions is given in the following table: Expressio s Interpretations = is equal to < is less than

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