2. WITHOUT using any calculator or pencil/pen, evaluate the following expressions: 901 + 00 + 357 439 + 0 4358 + 0 Subconsciously, you have applied the Additive Identity. The sum of any number and 0 is equal to the number. Thus, 0 is called the additive identity.
3. By understanding Additive Identity. What do you think is the Multiplicative Identity? Why? 1 is the multiplicative identity, since the product of any number and 1 is equal to the number itself.
4. Complete the following sentence: The product of any number and zero is equal to ______. This is known as the Multiplicative Property of Zero i.e. 8*0 15x0 a(0) (-7)(0)
5. Two numbers whose produce is 1 is known as ________. Reciprocals or Multiplicative inverses. An example of reciprocals would be: 2 / 7 and ____ ¾ and _____ ½ and _____ 5 and ____ 8 and _____ n and _____
10. Identity and Equality Properties Identity Properties Multiplicative identity Property For any number a, a 1 = 1 a = a. The product of any number and one is equal to that number. The number one is called the multiplicative identity. Example If a = 6 then 6 1 = 1 6 = 6
11. Identity and Equality Properties Identity Properties Multiplicative Property of Zero For any number a, a 0 = 0 a = 0. The product of any number and zero is equal to zero. Example If a = 6 then 6 0 = 0 6 = 0
12. Identity and Equality Properties Identity Properties Multiplicative Inverse Property Two numbers whose product is 1 are called multiplicative inverses or reciprocals. Zero has no reciprocal because any number times 0 is 0. Example
18. Identity and Equality Properties Equality Properties Symmetric Property of Equality For any numbers a and b, if a = b, then b = a. The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. Example If 10 = 7 + 3; then 7 +3 = 10 If a = b then b = a
19. Identity and Equality Properties Equality Properties For any numbers a, b and c, if a = b and b = c, then a = c. Transitive Property of Equality The transitive property of equality says that if one quantity equals a second quantity, and the second quantity equals a third quantity, then the first and third quantities are equal. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. Example If 8 + 4 = 12 and 12 = 7 + 5, then 8 + 4 = 7 + 5 If a = b and b = c , then a = c
20. Identity and Equality Properties Equality Properties Substitution Property of Equality If a = b, then a may be replaced by b in any expression. The substitution property of equality says that a quantity may be substituted by its equal in any expression. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. Example If 8 + 4 = 7 + 5; since 8 + 4 = 12 or 7 + 5 = 12; Then we can substitute either simplification into the original mathematical statement.
