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2.2 Add Real Numbers Goal • Add positive and negative numbers. Adding Integers Using a Number Line Graph the first number. If you are adding a positive number, move the absolute value of the second number to the right. If you are adding a negative number, move the absolute value of the second number to the left. We will do the first four together: 1) 3 + 5 = 2) -4 + -9 = 3) 2 + -12 = 4) -7 + 12 = Now work with your group to finish the rest of these problems. 5) -9 + 20 = 6) -9 + -6 = 7) 3 + -17 = Page 9) 3 + 12 = 1 8) 9 + -9 = 10) -11 + 12 = 13) Discuss what you found with your group. Try to summarize the rules for adding two integers by filling in the following sentences: A) When you add two positive numbers, ____________________ the absolute values of the numbers; the answer will always be _______________________. Show an example: B) When you add two negative numbers, ____________________ the absolute values of the numbers; the answer will always be _______________________. Show an example: c) When you add a positive number and a negative number, and the positive number is larger, ____________________ the absolute value of the smaller number from the absolute value of the larger number; use the sign of the _____________________ absolute value. Show an example: D) When you add a positive number and a negative number, and the negative number is larger, ____________________ the absolute value of the smaller number from the absolute value of the larger number; use the sign of the _____________________ absolute value. Show an example: 6) 18 + -20 = 2) 99 + -10 = 7) -25 + 50 = 3) -17 + -17 = 8) -10 + -33 = 4) -27 + 27 = 9) 24 + 36 + -75 = 5) -30 + -20 = 10) -12 + -12 + 13 = Page 1) -9 + 20 = 2 Now you try it! Now try these without a number line: PROPERTIES OF ADDITION Commutative Property of Addition The order in which you add two numbers does not change the sum. a + b = ___ + ___ Example: −1 + 3 =___+_____ Associative Property of Addition The way you group three numbers in a sum does not change the sum. (a + b) + c = ___ + (___ + ___) Example: (1 + 2) + 3 =___ + (___+___) Identity Property of Addition The sum of a number and 0 is the number. (You don’t change the identity of the number!) a + 0 = ___ + ___ = ___ Example: 4 + 0 = ___ Additive Identity is _____ because: Inverse Property The sum of a number and its opposite is 0. a + (−a) = ____ + ___ = ___ Example: −9 + ___ = 0 Additive Inverse is _____________________________________________________________ because: Now you try it! Identify the property demonstrated below: 1) -19 + 19 = 0 2) -19 + 19 = 19 + -19 3) -19 + 0 = -19 Page 3 4) -19 + (19 + 0) = (-19 + 19) + 0