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2-2 HW = Pg. 77-79 #12-50 e, 60-61 2-2 HW Continued 2-3 Subtraction of Real Numbers 1.) Subtraction can be turned into addition - adding the opposite of the second number is equivalent to subtracting the number 2.) Rules - a - b = a + (-b) Ex: 3 - 5 = 3 + (-5) = -2 Terms = parts of an expression that are separated by addition or subtraction signs - Ex: -9-2x has 2 terms, 4 y 7 x 9 has 3 terms 2 Important Rules to follow with Addition, DO NOT work for subtraction! • Commutative Property a b b a 5-4 4-5 • Associative Property a (b c) (a b) c 8-(7-6) (8-7)-6 • Property of Zero (Inverse Property) a (a) 0 8-(-8)=8+8=16 a-(-a) = a+a=2a This property STILL works for subtraction • Identity Property a –0=a Practice Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. Answers : 1.)4 5 4 (5) 1 • 1.) 4-5 2.)3 (8) 3 (8) 11 • 2.) 3-(-8) 3.)0 7 0 (7) 7 • 3.) 0-7 4.)2 (3) 2 (3) 5 2 1 1 2 1 1 • 4.) 2-(-3)-6 5.) ( ) ( ) ( ) 3 6 3 3 6 3 2 1 1 • 5.) ( ) 4 1 2 5 3 6 3 ( ) 6 6 6 6 Practice 2 Evaluate the expression 1.) 8-11-(-6) 2.) 3-(-8)+(-9) 3.) –7+42-63 4 2 5 4.) 6-1+10-(-8) 5.) ( ) 9 3 6 Find the terms of the expression 6.) -4-y 7.) -3x+6 8.) x-y-7 Evaluate the function for these values of x: -2, -1, 0, and 1. Organize your results in a table 9.) y = x - 8 10.) y = -x + 12 Practice 2 - Answers 1.) 8-11-(-6) = 8+(-11)+(+6) = 3 2.) 3-(-8)+(-9) = 3+(+8)+(-9) = 2 3.) –7+42-63= -7+42+(-63) = -28 4.) 6-1+10-(-8) = 6+(-1)+10+(+8) = 23 4 2 5 8 12 15 -35 17 5.) 9 3 ( 6 ) = - 18 ( 18 ) ( 18 ) = 18 118 6.) -4-y : 2 terms –4 and y 7.) -3x+6 : 2 terms –3x and 6 8.) x-y-7 : 3 terms x, -y and -7 9.) X -2 -1 0 1 10.) X -2 -1 0 Y -10 -9 -8 -7 Y 1 14 13 12 11 Summary • Adding the ___________ of a number is equivalent to subtracting the number. • The following properties DO NOT work for subtraction _______________, _______________, and _______________. • The ___________ ______________ is the only addition property that works for subtraction. • The parts in a expression separated by addition symbols are called___________. Check Yourself Pg. 82-84 #4-38 e, 42-44, 49-50 Quiz 1 Pg. 84 #1-10 and study for Ch.2 Quiz 1