Section 1.4 Addition of Real Numbers 43 Solutions 1a. We begin at 0, move right 7 units, and then right 2 more units. +7 +2 0 1 2 3 4 5 6 7 8 9 10 So, 7 + 2 = 9. 1b. We begin at 0, move left 1 unit, and then left 4 more units. (–4) (–1) –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 So, (-1) + (-4)=-5. 1c. (-2) + (-7)=-9 1d. (-1.5) + (-3)=-4.5 1 5 1e. + 3 10 = 2 10 + 3 10 = 5 10 = 1 2 1f. (-7) + a- 2 3 b = a- 7 1 b + a- 2 3 b = a- 21 3 b + a- 2 3 b =- 23 3 1g. (-8) + (-2) + (-4)=-14 Add the absolute values. u-2u + u-7u = 2 + 7 = 9 Use the sign of the original numbers. Add the absolute values. u-1.5u + u-3u = 1.5 + 3 = 4.5 Use the sign of the original numbers. Convert 1 5 to a fraction with a denominator of 10, 1 5 Add the absolute values. P 2 10 P + P 3 10 P = 2 10 Keep the sign of the original numbers. Simplify the result. Rewrite -7 as a fraction, - convert it to a fraction with a denominator of 3, - 7 1 =- 21 3 . Add the absolute values of the two numbers. P -21 3 P + P -2 3 P = Use the sign of the original numbers. Add the absolute values. u-8u + u-2u + u-4u = 8 + 2 + 4 = 14 Use the sign of the original numbers. Student Check 1 Add. For parts (a) and (b), use a number line to add the numbers. = 2 10 . + 3 10 = 5 10 7 1 , and 21 3 + 2 3 = a. 3 + 5 b. (-4) + (-3) c. (-2.6) + (-1.3) d. 23 3 2 3 + 1 6 e. a- 4 5 b + a- 7 15 b f. (-5) + a- 1 2 b g. (-5) + (-1) + (-6) Adding Numbers with Different Signs Adding real numbers with different signs occurs in many different situations. An everyday occurrence deals with temperature changes. Suppose the temperature at 7:00 a.m. in Duluth, Minnesota, one winter morning was 2°F below zero and the temperature rose 5°F Objective 2 ▶ Add numbers with different signs.
hendricks_beginning_algebra_1e_ch1_3
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