Lesson 1-4 Identity and Equality Properties Miss Simpson ADDITIVE IDENTITY Definition: Any number plus zero equals that number. a+ 0 = a 3+ 0 = = 1600 n + 0 = 18 What is the value of n? MULTIPLICATIVE IDENTITY Definition: Any number multiplied by one equals that number. a 1 = a 8 1 = 8 19 1 = 19 n 1 = 58 What is the value of n? MULTIPLICATIVE PROPERTY OF ZERO Definition: Any number multiplied by zero equals zero. a 0 = 0 = 0 31 0 = 0 n 15 = 0 What is the value of n? MULTIPLICATIVE INVERSE Definition: Any number multiplied by its reciprocal equals one. Which brings up the question: What is reciprocal? WHAT IS RECIPROCAL? Two numbers whose product is one. FLIP a number. What is the reciprocal of: = a b = 1 b a 7 9 = 1 = 1 n What is the value of n? REFLEXIVE PROPERTY Definition: Any quantity equals itself. a = a 9 = = = 2 + n What is the value of n? SYMEMETRIC PROPERTY Definition: If one quantity equals a second quantity, then the second quantity equals the first. If a = b, then b = a. If = 9, then 9 = If 8 = 4 2, then 4 2 = 8. If 2a = 10, then 10 = 2a. TRANSITIVE PROPERTY Definition: If one quantity equals a second and a second quantity equals a third, then the first equals the third. If a = b and b = c, then a = c. If = 5 and 5 = 4 + 1, then = If 5(6) = 3(10) and 3(10) = 30, then... SUBSTITUTION (SOLVE) PROPERTY Definition: A quantity may be substituted for its equal. If a = b, then a can be replaced by b. If n = 15, then 3n = 3(15) 5(9-7) = 5(?) 25 5 = ? NAME THAT PROPERTY. n + 0 = 19 NAME THAT PROPERTY. 28 a = 0 NAME THAT PROPERTY = f + 6 NAME THAT PROPERTY. 1 b = 23 NAME THAT PROPERTY. 1 x = 1 4 NAME THAT PROPERTY. 2(9 3) = 2(m) NAME THAT PROPERTY. 24 4 = y NAME THAT PROPERTY. n 9 = 9 NAME THAT PROPERTY. If = 12, then 12 = 8 + 4 NAME THAT PROPERTY. If 8(3) = 24 and 24 = 12(2), then 8(3) = c. NAME THAT PROPERTY. 7 + z = 7 NAME THAT PROPERTY. (8+ 7)(4) = r(4) EVALUATE. NAME PROPERTY. 7 + (16 4) 7 (16 16) - SUBSTITUTION 7 (1) - SUBSTITUTION 7 MULT. IDENTITY EVALUATE. NAME PROPERTY. 2(3 5 1 14) 4 2(15 1 14) - 4 - SUBSTITUTION 2(15 14) - 4 - MULT. IDENTITY 2(1) - 4 SUBSTITUTION MULT. IDENTITIY MULT. INVERSE 1 SUBSTITUTION EVALUATE. NAME PROPERTY. 2[5 (15 3)] 2[5 5] - SUBSTITUTION 2[0] - SUBSTITUTION 0- MULT. PROPERTY OF ZERO EVALUATE. NAME PROPERTY. 3(5 51) + 21 7 3(5 - 5 1) + 21 7 - SUBSTITUTION 3(5 5) + 21 7 - MULT. IDENTITY 3(0) + 21 7 SUBSTITUTION 7 MULT. PROP. OF ZERO SUBSTITUION 3 ADDITIVE IDENTITY EVALUATE. NAME PROPERTY. 4 3[7 (2 3)] 4 3[7 6] - SUBSTITUTION 4 3[1] - SUBSTITUTION 4 3 - MULT. IDENTITY 1- SUBSTITUTION