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Algebra 2 1.2: Operations on Real Numbers Adding Two Negative Numbers Add their absolute values, then put the negative sign in front: a) -12 + (-8) (12 8) 20 b) -6 + (-3) (6 3) 9 c) -1.2 + (-0.4) (1.2 0.4) 1.6 5 1 d) 5 1 5 2 7 6 3 6 6 3 6 6 Adding Numbers With Different Signs Find the difference of the absolute values, then give the answer the sign of the larger absolute value: a) -17 + 11 17 11 6 b) 4 + -1 4 1 3 c) -9 + 17 17 9 8 d) 4 2 12 10 12 10 2 5 3 15 15 15 15 15 Subtracting Real Numbers Change the subtraction to an addition, then follow the rules of addition: a) 6 – 8 6 (8) (8 6) 2 8 5 8 5 13 b) 3 3 3 3 3 Adding and Subtracting Real Numbers Work from left to right: a) -8 + 5 – 6 (8 5) 6 3 6 9 b) 15 – (-3) – 5 – 12 (15 3) 5 12 18 5 12 13 12 1 Multiplying Real Numbers The product of two numbers with the same sign is positive. The product of two numbers with different signs is negative. 3 5 a) 15 5 4 3 12 4 b) 2 3 6 2 3 3 1 3 2 3 Dividing Real Numbers To divide, multiply by the reciprocal of the second number (the number you are dividing by). The quotient of two nonzero numbers with the same sign is positive. The quotient of two nonzero numbers with different signs is negative. 1 12 a) 12 4 12 3 4 4 2 b) 3 2 5 2 9 18 6 5 3 9 3 5 15 5 9 CAUTION!!! 1. A number and its additive inverse always have the opposite sign. However, a number and its reciprocal always have the same sign. 2. Division by zero is undefined, however, zero can be divided by a nonzero number. Example: 6 undefined 0 0 0 6 Equivalent Forms of a Fraction x x x y y y Also : x x y y