Identity & Equality Properties (Algebra1 1_4)

Identity and Equality Properties

What You'll Learn Vocabulary 1) additive identity 2) multiplicative identity 3) multiplicative inverse 4) reciprocal Identity and Equality Properties ,[object Object],[object Object]

Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank.

Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. +

Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. 4 + r = 4 +

Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. 4 + r = 4 + The solution of this equation is 0. Oregon State’s rank changed by 0 from December 11 to the final rank.

Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. 4 + r = 4 + The solution of this equation is 0. Oregon State’s rank changed by 0 from December 11 to the final rank. In other words, 4 + 0 = 4 .

Identity and Equality Properties ,[object Object]

Identity and Equality Properties ,[object Object],a

Identity and Equality Properties ,[object Object],a ,[object Object]

Identity and Equality Properties ,[object Object],a ,[object Object],a

Identity and Equality Properties ,[object Object],a ,[object Object],a ,[object Object]

Identity and Equality Properties ,[object Object],a ,[object Object],a ,[object Object],7

Identity and Equality Properties ,[object Object],a ,[object Object],a ,[object Object],7 The sum of any number and 0 is equal to the number. This is called the _______________.

Identity and Equality Properties ,[object Object],a ,[object Object],a ,[object Object],7 The sum of any number and 0 is equal to the number. This is called the _______________. additive identity

Identity and Equality Properties There are also special properties associated with multiplication .

Identity and Equality Properties There are also special properties associated with multiplication . The solution of the equation is 1. Since the product of any number and 1 is equal to the number, 1 is called the _____________________

Identity and Equality Properties There are also special properties associated with multiplication . The solution of the equation is 1. Since the product of any number and 1 is equal to the number, 1 is called the _____________________ multiplicative identity

Identity and Equality Properties There are also special properties associated with multiplication . The solution of the equation is 1. Since the product of any number and 1 is equal to the number, 1 is called the _____________________ multiplicative identity The solution of the equation is 0. The product of any number and 0 is equal to 0. This is called the _____________________

Identity and Equality Properties There are also special properties associated with multiplication . The solution of the equation is 1. Since the product of any number and 1 is equal to the number, 1 is called the _____________________ multiplicative identity The solution of the equation is 0. The product of any number and 0 is equal to 0. This is called the _____________________ Multiplicative Property of Zero

Identity and Equality Properties There are also special properties associated with multiplication . Two numbers whose product is 1 are called _____________________ or ____________.

Identity and Equality Properties There are also special properties associated with multiplication . Two numbers whose product is 1 are called _____________________ or ____________. multiplicative inverses reciprocals

Identity and Equality Properties There are also special properties associated with multiplication . Two numbers whose product is 1 are called _____________________ or ____________. multiplicative inverses reciprocals is the multiplicative inverse (or reciprocal) of 5, and

Identity and Equality Properties There are also special properties associated with multiplication . Two numbers whose product is 1 are called _____________________ or ____________. multiplicative inverses reciprocals is the multiplicative inverse (or reciprocal) of 5, and 5 is the multiplicative inverse (or reciprocal) of

Identity and Equality Properties For any number a, the product of a and 1 is a. For any number a, the product of a and 0 is 0. Multiplicative Inverse Multiplicative Property of Zero Multiplicative Identity Examples Symbols Words Property

Identity and Equality Properties Any quantity is equal to itself. If one quantity equals a second quantity, then the second quantity equals the first. Symmetric Reflexive Examples Symbols Words Property

Identity and Equality Properties Any quantity is equal to itself. If one quantity equals a second quantity, then the second quantity equals the first. For any number a, a = a Symmetric Reflexive Examples Symbols Words Property

Identity and Equality Properties Any quantity is equal to itself. If one quantity equals a second quantity, then the second quantity equals the first. For any number a, a = a For any numbers a and b , If a = b then b = a Symmetric Reflexive Examples Symbols Words Property

Identity and Equality Properties If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. A quantity may be substituted for its equal in any expression. Substitution Transitive Examples Symbols Words Property

Identity and Equality Properties If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. A quantity may be substituted for its equal in any expression. For any numbers a, b, and c, If a = b and b = c, then a = c. Substitution Transitive Examples Symbols Words Property

Identity and Equality Properties If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. A quantity may be substituted for its equal in any expression. For any numbers a, b, and c, If a = b and b = c, then a = c. If 8 = 5 + 3 and 5 + 3 = 6 + 2, then 8 = 6 + 2. Substitution Transitive Examples Symbols Words Property

Identity and Equality Properties If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. A quantity may be substituted for its equal in any expression. For any numbers a, b, and c, If a = b and b = c, then a = c. For any numbers a and b, If a = b then a may be replaced by b in any expression. If 8 = 5 + 3 and 5 + 3 = 6 + 2, then 8 = 6 + 2. Substitution Transitive Examples Symbols Words Property

Identity and Equality Properties If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. A quantity may be substituted for its equal in any expression. For any numbers a, b, and c, If a = b and b = c, then a = c. For any numbers a and b, If a = b then a may be replaced by b in any expression. If 8 = 5 + 3 and 5 + 3 = 6 + 2, then 8 = 6 + 2. If n = 12, then 3 n = 36 Substitution Transitive Examples Symbols Words Property

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Identity & Equality Properties (Algebra1 1_4)

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Identity & Equality Properties (Algebra1 1_4)