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Transcript
FINDING ABSOLUTE VALUE AND ADDING/SUBTRACTING REAL NUMBERS THE NUMBER SYSTEM, EXPRESSIONS AND EQUATIONS WARM-UP 1. The set of _________________ includes all rational and irrational numbers. 2. 54.2 − 27.38 3. 1 2 + 3 8 4. 1.09 + 76.9 5. 3 4 − 3 8 CORRECTING HOMEWORK Remember cheating is not okay and not worth it. Be fair and honest. Be kind. Don’t forget to put “C.B. ___________” with your name. Trade with a neighbor. “NEW” STUFF The absolute value of a number is its distance from 0 on a number line. Absolute value is denoted using vertical bars, e.g. 4 means “the absolute value of 4” Because it is a distance, absolute value is always positive. EXAMPLE a. |0| b. | − 7.12| c. 3 1−4 d. −|11 − 2| ADDING AND SUBTRACTING REAL NUMBERS Rules for Adding Real Numbers To add numbers with the same sign, add their absolute values. The sum will have the original sign. To add numbers with different signs, find the difference of their absolute values. The sum will have the sign of the larger number. A little song to help you remember: (to the tune of Row, Row, Row Your Boat) Same signs, add and keep Different signs, subtract Keep the sign of the larger number Then you’ll be exact. SUBTRACTING REAL NUMBERS Two numbers with the same absolute value but different signs are opposites or additive inverses of each other. The sum of a number and its inverse is 0. Inverse Property of Addition: For every real number 𝑎, 𝑎 + −𝑎 = −𝑎 + 𝑎 = 0 Rules for Subtracting Real Numbers To subtract a real number, add its inverse. Then follow the rules for adding real numbers. EXAMPLES Simplify. a. (−12) + 21 b. −19 + (−8) c. 3.2 − −5.1 d. −13 − 12 EXAMPLES FROM THE REAL WORLD On the first down, the Aggies lost 4 yards. They gained 7 yards on the second down. What was their total yard gain (or loss)? Dr. Hodgens collected a water sample at a depth of 23 meters from the surface. He descended another 12 meters to collect a plant sample. Where was Dr. Hodgens in relation to the surface when he retrieved the plant sample? LESSON PRACTICE a. −3.4 b. −23.4 + 18.72 c. − 2 3 + − 1 6 d. 14 − (−22) e. f. − 2 3 − − 1 6 The set of real numbers is closed under addition. g. The set of real numbers is closed under subtraction. h. The set of integers is closed under subtraction. HOMEWORK 1st and 2nd periods: Pg. 29-30 #1-30 3rd period: Pg. 25-26 #1-15