Elementary and Intermediate Algebra by M. Dugopolski PDF

By M. Dugopolski

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A letter that is used to represent a number is called a variable because its value may vary. For example, we might say that a and b are integers. This means that a and b could be any of the infinitely many possible integers. They could be different integers or they could even be the same integer. We will use variables to describe the next set of numbers. a The set of rational numbers consists of all possible ratios of the form ᎏbᎏ, where a and b are integers, except that b is not allowed to be 0.

To construct a number line, we draw a straight line and label any convenient point with the number 0. Now we choose any convenient length and use it to locate other points. Points to the right of 0 correspond to the positive numbers, and points to the left of 0 correspond to the negative numbers. Zero is neither positive nor negative. The number line is shown in Fig. 3. 3 The numbers corresponding to the points on the line are called the coordinates of the points. The distance between two consecutive integers is called a unit and is the same for any two consecutive integers.

Of course ᎏᎏ times ᎏᎏ 3 6 1 6 3 1 2 is also ᎏᎏ. So dividing by 2 is equivalent to multiplying by ᎏᎏ. In symbols: 1 1 2 1 1 1 ᎏᎏ Ϭ 2 ϭ ᎏᎏ Ϭ ᎏᎏ ϭ ᎏᎏ · ᎏᎏ ϭ ᎏᎏ 3 3 1 3 2 6 The pizza example illustrates the general rule for dividing fractions. Division of Fractions If b 0, c 0, and d 0, then a c a d ᎏᎏ Ϭ ᎏᎏ ϭ ᎏᎏ и ᎏᎏ. qxd 9/14/10 9:45 AM Page 18 18 1-18 Chapter 1 Real Numbers and Their Properties In general if m Ϭ n ϭ p, then n is called the divisor and p (the result of the m division) is called the quotient of m and n.

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Elementary and Intermediate Algebra by M. Dugopolski

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