after 3 hr. The temperature at 10 a.m. can be found by simplifying the expression -2°F + 5°F. To perform this operation, we will use a thermometer. We begin at 0°F and go down to -2°F and then go up by 5°F. This takes us to 3°F. So, we have -2 + 5 = 3 We can also obtain the same result by using a number line as well. (+5) (–2) –4 –3 –2 –1 0 1 2 3 4 5 6 Suppose the temperature is 5°F at 12:00 a.m. and the temperature fell 8°F in 2 hr. To determine the temperature at 2:00 a.m., we need to find the result of 5°F + (-8)°F. The thermometer can assist us again. In this case, we begin at 0°F, and go up by 5°F and then go down 8°F. This takes us to -3°F. So, we have 5 + (-8)=-3 Again, we can obtain the same result by using a number line. (–8) (+5) –4 –3 –2 –1 0 1 2 3 4 5 6 5 0 1 2 43 –1 –2 –3 –4 5 0 1 2 43 –1 –2 –3 –4 From these examples, we conclude that adding numbers with opposite signs can result in either a positive or negative number. The final sign is actually determined by the sign of the number with the larger absolute value. In the first example, 5 is the number with the larger absolute value and the sign of the -2 + 5 is positive. In the second example, -8 is the number with the larger absolute value and the sign of 5 + (-8) is negative. ���������������������� Adding Numbers with Different Signs Step 1: Subtract the absolute values of the numbers. Step 2: The sign of the result is the same as the sign of the number with the larger absolute value. �� ������������������������ ������������������ Add. For parts (a) and (b), use a number line to add the numbers. 2a. 3 + (-2) 2b. (-7) + 4 2c. 20 + (-35) 2d. -14 + 15.5 2e. -7 + 7 2f. a- 1 4 b + 2 3 2g. (-9) + 5 + (-2) Solutions 2a. We begin at 0 and move right 3 units and then left 2 units. (–2) (+3) 0 1 2 3 4 5 6 So, 3 + (-2) = 1. –5 (+5) (–8) –5 (–2) (+5) 44 Chapter 1 Real Numbers and Algebraic Expressions
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