Section 1.4 identity and equality properties (algebra)

Section 1.4 identity and equality properties (algebra)

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  Section 1.4Identity andEquality Properties
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  WITHOUT using anycalculator or pencil/pen, evaluate the following expressions:901 + 00 + 357 439 + 0 4358 + 0Subconsciously, 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.
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  By understanding AdditiveIdentity. 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.
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  Complete the followingsentence:The product of any number and zero is equal to ______.This is known as the Multiplicative Property of Zeroi.e.8*0 15x0 a(0) (-7)(0)
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  Two numbers whoseproduce 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 _____
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  Identity and EqualityPropertiesIdentity PropertiesAdditive Identity Property
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  Multiplicative Identity Property
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  Multiplicative Identity Propertyof Zero
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  Multiplicative Inverse PropertyIdentityand Equality PropertiesIdentity PropertiesAdditive Identity PropertyFor any number a, a + 0 = 0 + a = a.The sum of any number and zero is equal to that number.The number zero is called the additive identity.ExampleIf a = 5 then 5 + 0 = 0 + 5 = 5
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  Identity and EqualityPropertiesIdentity PropertiesMultiplicative identity PropertyFor 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.ExampleIf a = 6 then 6  1 = 1  6 = 6
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  Identity and EqualityPropertiesIdentity PropertiesMultiplicative Property of ZeroFor any number a, a  0 = 0  a = 0.The product of any number and zero is equal to zero.ExampleIf a = 6 then 6  0 = 0  6 = 0
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  Identity and EqualityPropertiesIdentity PropertiesMultiplicative Inverse PropertyTwo numbers whose product is 1 are called multiplicative inverses or reciprocals.Zero has no reciprocal because any number times 0 is 0.Example
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  Identity and EqualityPropertiesEquality PropertiesEquality Properties allow you to compute with expressions on both sides of an equation by performing identical operations on both sides of the equation. This creates a balance to the mathematical problem and allows you to keep the equation true and thus be referred to as a property. The basic rules to solving equations is based on these properties. Whatever you do to one side of an equation; You must perform the same operation(s) with the same number or expression on the other side of the equals sign.
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  Reflexive Property ofEquality
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  Symmetric Property ofEquality
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  Transitive Property ofEquality
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  Substitution Property ofEqualityIdentity and Equality PropertiesEquality PropertiesReflexive Property of EqualityFor any number a, a = a.The reflexive property of equality says that any real number is equal to itself. 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.ExampleIf a = a ; then 7 = 7; then 5.2 = 5.2
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  Identity and EqualityPropertiesEquality PropertiesSymmetric Property of EqualityFor 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.ExampleIf 10 = 7 + 3; then 7 +3 = 10If a = b then b = a
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  Identity and EqualityPropertiesEquality PropertiesFor any numbers a, b and c, if a = b and b = c, then a = c.Transitive Property of EqualityThe 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.ExampleIf 8 + 4 = 12 and 12 = 7 + 5, then 8 + 4 = 7 + 5If a = b and b = c , then a = c
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  Identity and EqualityPropertiesEquality PropertiesSubstitution Property of EqualityIf 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.ExampleIf 8 + 4 = 7 + 5; since 8 + 4 = 12 or 7 + 5 = 12;Then we can substitute either simplification into the original mathematical statement.
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  ClassworkPAGE 23 #12 – 28 ALLHomeworkPAGE 25 # 44 – 62 EVEN