VIEWS: 2 PAGES: 25 POSTED ON: 11/20/2012
Problem of the Day Copy and complete the magic square. The magic sum is 0. +5 –8 +3 –2 0 +2 –3 +8 –5 Monday, November 19, 2012 Homework Answers -Integer, additive inverse, opposite, absolute value 15) -3 < 2, Mon, Thurs, Tues, Wed 37) -16, -12, 24 17) -11,-5, 8 39) -45, -25, 35 19) -2, -1, 4 41) 50 21) 15 43) 1 23) 31 45) 72 25) 21 47) 6 27) 10 49) 48 29) < 51) 2 31) = 55) The absolute value of a 33) = number is always positive. 35) > 56) -7, -6, -5 Integers are the set of whole numbers and their opposites. On a number line, opposites, or additive inverses, are numbers that are the same distance from 0, but on opposite sides of 0 on the number line. Remember! Numbers on a number line increase in value as you move from left to right. –5 –4 –3 –2 –1 0 1 2 3 4 5 What integer would represent each situation? 1) 160 ft below sea level 2) a gain of 13 yards 3) John earned $35 4) Alaska’s temperature was 5 below zero 5) a loss of 10 yards 6) Betsy spent $55 A number’s absolute value is its distance from 0 on a number line. Absolute value is always positive because distance is always positive. “The absolute value of –4” is written as –4 . Additive inverses have the same absolute value. 4 units 4 units –5 –4 –3 –2 –1 0 1 2 3 4 5 –4 = 4 = 4. Since absolute value is only concerned with distance, not direction, the absolute value of a number cannot be negative. Examples: 7 = 7 -14= 14 -24 = 24 10 - 8 = 2 Name two integers whose absolute value is 9. WATCH: Evaluate each expression. A. –8 + –5 –8 = 8 –8 is 8 units from 0. –5 = 5 –5 is 5 units from 0. 8 + 5 = 13 B. 5 – 6 –1 = 1 –1 is 1 units from 0. Evaluate each expression. A. –4 + 6 B. 12 + -8 C. 5 + 10 D. -1 + -11 Monday, November 19, 2012 EX. 1- Use a number line to find the sum. (–6) + 2 –6 2 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 You finish at –4, so (–6) + 2 = –4. Helpful Hint To add a positive number move to the right. To add a negative number move to the left. EX. 2- Use a number line to find the sum. –3 + (–6) –6 -3 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 You finish at –9, so –3 + (–6) = –9. Rules for Adding Integers Same signs, find the SUM. The answer carries the same sign. Example: Example: 18 + 4 = 22 (-18) + (-4) = -22 Different signs, find the DIFFERENCE. The answer carries the sign of the number with the greater absolute value. Example: Example: (-8) + 4 = -4 (-4) + 8 = 4 Melissa opened a new bank account. Find her account balance after the first four transactions listed below. Deposits: $200, $20 Withdrawals: $166, $38 200 + 20 + (–166) + (–38) Use a positive sign for deposits and a negative sign for withdrawals. 220 + (–204) 16 Melissa’s account balance after the first four transactions is $16. Note that each of the following statements is true: 10 – 5 = 10 + (-5) 7 – 7 = 7 + (-7) 25 – 10 = 25 + (-10) What do you notice about the first expression in each equality and its relationship to the 2nd expression? Subtracting an integer is the same as adding its opposite. Change the subtraction sign to an addition sign and change the sign of the second number. The rules for subtracting integers are: *change subtraction to addition *change the sign of the second integer *now follow the rules for adding integers with like or unlike signs Subtracting an integer is the same as adding its opposite. Change the subtraction sign to an addition sign and change the sign of the second number. A. –7 – 4 B. 8 – (–5) C. –6 – (–3) Subtract Examples D. –7 – (–8) E. –4 – 1 F. 3 – (–6) The top of the Sears Tower in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? 1454 – (–43) Subtract the lowest level from the height. 1454 + 43 Add the opposite of (–43). = 1497 Same sign; use the sign of the integers. The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool? 10 – (–12) Subtract the depth of the pool from the height of the high dive. 10 + 12 Add the opposite of (–12). = 22 It is 22 feet from the diving board to the bottom of the pool. Examples: 1)-4 – 2 2) -4 – (-2) 3)-8 – 9 4) 3 – (-2) – 4 5) - 2 – 4 6) -2 - 4 7) Use algebra tiles to show a model of the result of #2. Be sure to write an addition problem first!!! -4 – (-2) Homework Worksheet 1.2 Human Number Line Adding – face right Subtracting – face left Positive number – walk forward Negative number – walk backward 3+6= 3 - 6= -3 + 6 = -3 – 6 = 3 + -6 = 3 - -6= -3 + -6 = -3 - -6=