Section 1.4 Addition of Real Numbers 45 2b. We begin at 0 and move left 7 units and then right 4 units. (+4) (–7) –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 So, (-7) + 4 = -3. 2c. 20 + (-35) = -15 Subtract the absolute values of the numbers. u20u = 20, u-35u = 35, 35 - 20 = 15 Since u-35u > u20u , the sign of the answer is negative. 2d. -14 + 15.5 = 1.5 Subtract the absolute values of the numbers. u-14u = 14, u15.5u = 15.5, 15.5 - 14 = 1.5 Since u15.5u > u-14u, the sign of the answer is positive. 2e. -7 + 7 = 0 Subtract the absolute values of the numbers. u-7u = 7, u7u = 7, 7 - 7 = 0 Since the difference of the absolute values is zero, the sign of the answer is neither positive nor negative. 2f. a- 1 4 b + 2 3 =- 3 12 + 8 12 = 5 12 Rewrite each fraction with a denominator of 12. - 1 4 =- 3 12 nd 2 3 = 8 12 Subtract the absolute values of the numbers. P- 3 12 P = 3 12 , P 8 12 P = 8 12 , 8 12 - 3 12 = 5 12 Since P 8 12 P > P- 3 12 P , the sign of the answer is positive. 2g. (-9) + 5 + (-2) = -4 + (-2) Add the fi rst two numbers. Their signs are different so we subtract their absolute values and keep the sign of the number with the larger absolute value. u-9u = 9, u5u = 5, 9 - 5 = 4 u-9u > u5u S(-9) + 5=-4 Add the result and the last number. Their signs are the same, so we add their absolute values and keep the sign of the original numbers. u-4u = 4, u-2u = 2, 4 + 2 = 6 Since the numbers are negative, the result is negative. = -6 Student Check 2 Add the numbers. a. 2 + (-10) b. -4 + 8 c. (-16) + 4 d. 18.4 + (-6.2) e. 3 + (-3) f. 3 8 + a- 5 4 b g. 12 + (-2) + (-6) Applications Addition of real numbers occurs in many different aspects of real life. We find adding real numbers when balancing checkbooks, determining net worth, determining values of stocks, calculating golf scores, calculating total gain/loss in yardage for football plays, changes in temperature, changes in elevation, and so on. Objective 3 ▶ Solve real-life problems.
hendricks_beginning_algebra_1e_ch1_3
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