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Algebra IA Ch.1: Foundations for Algebra 1.5 Adding and Subtracting Real Numbers Sum – the answer when you add Template Ex.1: What is each sum? Use a number line, if necessary. a. 8 + 4 b. 8 + (-4) c. -8 + 4 d. -8 + (-4) Absolute Value – the distance a number is from zero on a number line. Therefore, absolute value can never be negative. Symbol - │x│ Examples: Situation Positive + Positive 7+2 Negative + Negative -7 + -2 Positive + Negative 7 + -2 Negative + Positive -7 + 2 Rules for addition Rule Just add Take the absolute value of each. Add. Attach the negative sign. Take the absolute value of each. Subtract the smaller from the larger. Attach the original sign of the larger absolute value. Take the absolute value of each. Subtract the smaller from the larger. Attach the original sign of the larger absolute value. Greatest Absolute Value Rules! Ex.2: What is each sum? Use absolute value, if necessary. a. -16 + (-8) b. -11 + 9 c. 9.2 + (-11.3) d. 2 1 3 4 Opposites – 2 values whose sum is zero. Also called Additive Inverses -a is read “the opposite of a” -(-2) = 2 -(5) = -5 -(0) = 0 Inverse Property of Addition – a + a = 0 Difference – answer when you subtract Rule for subtraction – subtraction is the same as adding the opposite Ex.3: What is each difference? a. -8 – (-13) b. 9 – 9 c. 12 – 14 d. -11 – 15 Ex.4: For what values of a and b does a b b a . Ex.5: A robot submarine dives 803 feet to the ocean floor. It rises 215 feet as the water gets shallower. Then the submarine dives 2619 feet into a deep crevice. Next, it rises 734 feet to photograph a crack in the wall of the crevice. What is the location of the crack in relation to sea level? HW: pg.41 11-40, 55-65 (no calculator)