Identity & Equality Properties (Algebra1 1_4)

Slide 2: Identity and Equality Properties  Recognize the properties of identity and equality.  Use the properties of identity and equality. 1) additive identity 2) multiplicative identity 3) multiplicative inverse 4) reciprocal

Slide 3: Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank.

Slide 4: Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. + Rank on increase final rank for Dec.11 in rank season equals plus          

Slide 5: Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. + Rank on increase final rank for Dec.11 in rank season equals plus           r 4 + = 4

Slide 6: Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. + Rank on increase final rank for Dec.11 in rank season equals plus           r 4 + = 4 The solution of this equation is 0. Oregon State’s rank changed by 0 from December 11 to the final rank.

Slide 7: Identity and Equality Properties The open sentence below represents the change in rank of Oregon State from December 11 to the final rank. + Rank on increase final rank for Dec.11 in rank season equals plus           r 4 + = 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.

Slide 8: Identity and Equality Properties  For any number a, the sum of a and 0 is ___.

Slide 9: Identity and Equality Properties a  For any number a, the sum of a and 0 is ___.

Slide 10: Identity and Equality Properties a  For any number a, the sum of a and 0 is ___.  a+0 = 0+a = ___.

Slide 11: Identity and Equality Properties a  For any number a, the sum of a and 0 is ___. a  a+0 = 0+a = ___.

Slide 12: Identity and Equality Properties a  For any number a, the sum of a and 0 is ___. a  a+0 = 0+a = ___.  7+0 = 0+7 = ___.

Slide 13: Identity and Equality Properties a  For any number a, the sum of a and 0 is ___. a  a+0 = 0+a = ___. 7  7+0 = 0+7 = ___.

Slide 14: Identity and Equality Properties a  For any number a, the sum of a and 0 is ___. a  a+0 = 0+a = ___. 7  7+0 = 0+7 = ___. The sum of any number and 0 is equal to the number. This is called the _______________.

Slide 15: Identity and Equality Properties a  For any number a, the sum of a and 0 is ___. a  a+0 = 0+a = ___. 7  7+0 = 0+7 = ___. The sum of any number and 0 is equal to the number. This is called the _______________. additive identity

Slide 16: Identity and Equality Properties There are also special properties associated with multiplication.

Slide 17: Identity and Equality Properties There are also special properties associated with multiplication. 7n  7

Slide 18: Identity and Equality Properties There are also special properties associated with multiplication. 7n  7 The solution of the equation is 1. Since the product of any number and 1 is equal to the number, 1 is called the _____________________

Slide 19: Identity and Equality Properties There are also special properties associated with multiplication. 7n  7 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 _____________________

Slide 20: Identity and Equality Properties There are also special properties associated with multiplication. 7n  7 8n  0 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 _____________________

Slide 21: Identity and Equality Properties There are also special properties associated with multiplication. 7n  7 8n  0 The solution of the equation is 0. The solution of the equation is 1. The product of any number Since the product of any number and 0 is equal to 0. and 1 is equal to the number, This is called the 1 is called the multiplicative identity _____________________ _____________________

Slide 22: Identity and Equality Properties There are also special properties associated with multiplication. 7n  7 8n  0 The solution of the equation is 0. The solution of the equation is 1. The product of any number Since the product of any number and 0 is equal to 0. and 1 is equal to the number, This is called the 1 is called the Multiplicative Property multiplicative identity _____________________ of Zero _____________________

Slide 23: Identity and Equality Properties There are also special properties associated with multiplication. 1 5 1 5

Slide 24: Identity and Equality Properties There are also special properties associated with multiplication. 1 5 1 5 Two numbers whose product is 1 are called _____________________ or ____________.

Slide 25: Identity and Equality Properties There are also special properties associated with multiplication. 1 5 1 5 Two numbers whose product is 1 are called _____________________ or ____________. multiplicative inverses reciprocals

Slide 26: Identity and Equality Properties There are also special properties associated with multiplication. 1 5 1 5 Two numbers whose product is 1 are called _____________________ or ____________. multiplicative inverses reciprocals 1 is the multiplicative inverse (or reciprocal) of 5, and 5

Slide 27: Identity and Equality Properties There are also special properties associated with multiplication. 1 5 1 5 Two numbers whose product is 1 are called _____________________ or ____________. multiplicative inverses reciprocals 1 is the multiplicative inverse (or reciprocal) of 5, and 5 1 5 is the multiplicative inverse (or reciprocal) of 5

Slide 28: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the Identity product of a and 1 is a. Multiplicative For any number a, the Property product of a and 0 is 0. of Zero a Multiplicative For any number , b Inverse where a, b  0, there is b exactly one number a such that the product of a b and is 1. b a

Slide 29: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the x *1  x Identity product of a and 1 is a. Multiplicative For any number a, the Property product of a and 0 is 0. of Zero a Multiplicative For any number , b Inverse where a, b  0, there is b exactly one number a such that the product of a b and is 1. b a

Slide 30: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the 13 *1  13 x *1  x Identity product of a and 1 is a. Multiplicative For any number a, the Property product of a and 0 is 0. of Zero a Multiplicative For any number , b Inverse where a, b  0, there is b exactly one number a such that the product of a b and is 1. b a

Slide 31: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the 13 *1  13 x *1  x Identity product of a and 1 is a. Multiplicative For any number a, the y *0  0 Property product of a and 0 is 0. of Zero a Multiplicative For any number , b Inverse where a, b  0, there is b exactly one number a such that the product of a b and is 1. b a

Slide 32: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the 13 *1  13 x *1  x Identity product of a and 1 is a. Multiplicative For any number a, the y *0  0 7*0  0 Property product of a and 0 is 0. of Zero a Multiplicative For any number , b Inverse where a, b  0, there is b exactly one number a such that the product of a b and is 1. b a

Slide 33: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the 13 *1  13 x *1  x Identity product of a and 1 is a. Multiplicative For any number a, the y *0  0 7*0  0 Property product of a and 0 is 0. of Zero a Multiplicative For any number ,  y  x  b Inverse     1 x  y  where a, b  0, there is   b exactly one number a such that the product of a b and is 1. b a

Slide 34: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the 13 *1  13 x *1  x Identity product of a and 1 is a. Multiplicative For any number a, the y *0  0 7*0  0 Property product of a and 0 is 0. of Zero a Multiplicative For any number ,  y  x   1  2  b Inverse     1     1 x  y  where a, b  0, there is  2  1    b exactly one number a such that the product of a b and is 1. b a

Slide 35: Identity and Equality Properties Property Words Symbols Examples Multiplicative For any number a, the 13 *1  13 x *1  x Identity product of a and 1 is a. Multiplicative For any number a, the y *0  0 7*0  0 Property product of a and 0 is 0. of Zero a Multiplicative For any number ,  y  x   1  2  b Inverse     1     1 x  y  where a, b  0, there is  2  1    b exactly one number a  7  3      1 such that the product of  3  7  a b and is 1. b a

Slide 36: Identity and Equality Properties Property Words Symbols Examples Reflexive Any quantity is equal to itself. Symmetric If one quantity equals a second quantity, then the second quantity equals the first.

Slide 37: Identity and Equality Properties Property Words Symbols Examples Reflexive For any number a, Any quantity is equal to itself. a=a Symmetric If one quantity equals a second quantity, then the second quantity equals the first.

Slide 38: Identity and Equality Properties Property Words Symbols Examples Reflexive For any number a, Any quantity is equal to itself. 99 a=a Symmetric If one quantity equals a second quantity, then the second quantity equals the first.

Slide 39: Identity and Equality Properties Property Words Symbols Examples Reflexive For any number a, Any quantity is equal to itself. 99 a=a Symmetric If one quantity equals a For any numbers second quantity, then a and b, the second quantity equals the first. a=b If then b = a

Slide 40: Identity and Equality Properties Property Words Symbols Examples Reflexive For any number a, Any quantity is equal to itself. 99 a=a Symmetric If one quantity equals a For any numbers second quantity, then If 3  8  11 a and b, the second quantity then 11  3  8 equals the first. a=b If then b = a

Slide 41: Identity and Equality Properties Property Words Symbols Examples Transitive If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. Substitution A quantity may be substituted for its equal in any expression.

Slide 42: Identity and Equality Properties Property Words Symbols Examples Transitive If one quantity equals For any numbers a second quantity, and a, b, and c, the second quantity equals a third quantity, a=b If then the first quantity and b = c, equals the third quantity. then a = c. Substitution A quantity may be substituted for its equal in any expression.

Slide 43: Identity and Equality Properties Property Words Symbols Examples Transitive If one quantity equals For any numbers 8=5+3 If a second quantity, and a, b, and c, and 5 + 3 = 6 + 2, the second quantity then 8 = 6 + 2. equals a third quantity, a=b If then the first quantity and b = c, equals the third quantity. then a = c. Substitution A quantity may be substituted for its equal in any expression.

Slide 44: Identity and Equality Properties Property Words Symbols Examples Transitive If one quantity equals For any numbers 8=5+3 If a second quantity, and a, b, and c, and 5 + 3 = 6 + 2, the second quantity then 8 = 6 + 2. equals a third quantity, a=b If then the first quantity and b = c, equals the third quantity. then a = c. Substitution A quantity may be For any numbers substituted for its equal a and b, in any expression. a=b If then a may be replaced by b in any expression.

Slide 45: Identity and Equality Properties Property Words Symbols Examples Transitive If one quantity equals For any numbers 8=5+3 If a second quantity, and a, b, and c, and 5 + 3 = 6 + 2, the second quantity then 8 = 6 + 2. equals a third quantity, a=b If then the first quantity and b = c, equals the third quantity. then a = c. Substitution A quantity may be For any numbers n = 12, If substituted for its equal a and b, in any expression. = 36 then 3n a=b If then a may be replaced by b in any expression.

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