b. pq When substituting a number for a variable, use parentheses. Substitute . Write the whole number as a fraction. Multiply fractions. Simplify. 1 21 2 3 Skill Practice Evaluate the algebraic expressions when x 5 and y 2. 2. 20 y 3. xy 2. The Set of Real Numbers Typically, the numbers represented by variables in an algebraic expression are all part of the set of real numbers. These are the numbers that we work with on a day-to-day basis.The real numbers encompass zero, all positive, and all negative numbers, including those represented by fractions and decimal numbers.The set of real numbers can be represented graphically on a horizontal number line with a point labeled as 0. Positive real numbers are graphed to the right of 0, and negative real numbers are graphed to the left of 0. Zero is neither positive nor negative. Each point on the number line corresponds to exactly one real number. For this reason, this number line is called the real number line (Figure 1-5). 5 4 3 2 1 0 Plotting Points on the Real Number Line Example 3 Plot the numbers on the real number line. a. b. c. d. Solution: a. Because is negative, it lies three units to the left of 0. b. The fraction can be expressed as the mixed number , which lies halfway between 1 and 2 on the number line. c. The negative number lies unit to the left of on the number line. d. The fraction can be expressed as the mixed number , which lies unit to the right of 3 on the number line. 2 6 5 4 3 2 1 0 1 2 3 3 4 5 5 6 16 4.7 3 15 315 16 5 7 4 4.7 10 112 3 2 3 16 5 4.7 3 2 3 3 1 4 1 1 3 41 p 4 and q 34 142 a 3 4 b Section 1.2 Introduction to Algebra and the Set of Real Numbers 23 1 2 3 4 5 Negative numbers Positive numbers Figure 1-5 Answers 2. 18 3. 10
miller_beginning_intermediate_algebra_4e_ch1_3
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