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Objective • The learner will add and subtract real numbers Lessons 2-2 Adding Real Numbers Pages 24 - 31 Subtracting Real Numbers Pages 32 - 36 Addition Rules • Like or Same Signs Add the numbers and keep the sign Ex) 3 + 5= 8 -4 + -1= -5 • Unlike or Different Signs Find the difference (subtract) their absolute values. The result has the sign of the number with largest absolute value Ex) -10 + 3 = -7 8 + (-4) = 4 Note: Keep the sign of the number that is furthest from zero Example #1 You can use number lines as models to add real numbers. Let’s try these together: • -6 + 4 c. 3 + 2 b. 4 + (-5) d. -5 + (-9) Now you try: • -3 + (-8) c. -2 + 1 b. 9 + (-3) d. 7 + 4 Subtraction Rule • Add its opposite!! Change the subtraction sign to an addition sign and switch the sign of the number that follows it. Ex) - 5 - 4 = -5 + -4 = 9 (-2) - (-3) = (-2) + 3 = 1 Note: You are not subtracting the FIRST number; therefore you DO NOT change the sign of the first number, only the one being subtracted (the second number) Example #1 You can use a number line to subtract numbers just like you used it to add numbers. Let’s try these together a. 2 – 6 b. -1 – 4 Now its your turn a. -3 – 8 b. 7 – 2 Videos • Subtracting Positive & Negative Numbers • Subtracting Double Negative Numbers Example #3 A football team gains 2 yds and then loses 7 yds in two plays. You express a loss of 7 yd as -7. Use addition to find the result of the two plays. 2 + (-7) = -5 The result of both plays is a loss of 5 yards. Now you try: The temperature falls 15 degrees and then rises 18 degrees. Use addition to find the change in temperature. Applying Addition You can evaluate expressions that involve addition. Substitute a value for the variable(s). Then simplify the expression. Example #4 Evaluate –n + 8.9 for n = -2.3 -n + 8.9 = - (-2.3) + 8.9 (Substitute -2.3 for n) = 2.3 + 8.9 (two negatives make positive) = 11.2 (Simplify) Now you try: Evaluate each expression for t = -7.1 a. b. c. d. t + (-4.3) -2 + t 8.5 + (-t) -t + 7.49 Example #5 A rock climber climbs a mountain. The base of the mountain is 132 ft below sea level. a. Write an expression to represent the climber’s height below or above sea level. Relate: 132 ft below sea level plus feet the route rises Define: let h = feet the route rises Write: -132 + h Your expression would be -132 + h Example #5 cont. Find the climber’s height above sea level when he is 485 ft above the base of the mountain. -132 + h = -132 + 485 (Substitute 485 for h) = 353 (Simplify) The climber’s height is 353 above sea level. Now you try: The temperature one winter morning is -14 degrees. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 11 degrees. When you simplify an expression, you work within grouping symbols first. Absolute value symbols are grouping symbols. Therefore, find the value of an expression within the absolute value signs before finding the absolute value. Example #4 Simplify | 5 – 11 | | 5 – 11 | = | -6 | (Subtract within abs. value) = 6 (absolute value of -6 is 6) Now you try: Simplify each expression: a. b. c. d. |8–7| |7–8| | -10 – (-4) | | -4 – (-10) | Now you try: Evaluate each expression for t = -2 and r = -7. a. r – t b. t – r c. - t – r d. - r – (- t) Now you try: Find the closing stocks of ABC and PQR on Wednesday.