1 6 Ident Equal Prop

8/3/2019 1 6 Ident Equal Prop

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Properties refer to rules that indicate astandard procedure or method to be followed.

A proof is a demonstration of the truth of astatement in mathematics.

Properties or rules in mathematics are theresult from testing the truth or validity ofsomething by experiment or trial to establish aproof.

Therefore every mathematical problem fromthe easiest to the more complex can be solvedby following step by step procedures that are

identified as mathematical properties.


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Additive Identity Property

Multiplicative Identity Property

Multiplicative Identity Property of Zero

Multiplicative Inverse Property


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Additive IdentityProperty

For any number a, a + 0 = 0 + a = a.

If a = 5 then 5 + 0 = 0 + 5 = 5

The sum of any number and zero is equal to that number.

The number zero is called the additive identity.


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Multiplicativeidentity Property

For any number a, a 1 = 1 a = a.

If a = 6 then 6 1 = 1 6 = 6

The product of any number and one is equal to that number.

The number one is called the multiplicative identity.


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MultiplicativeProperty of Zero

For any number a, a 0 = 0 a = 0.

If a = 6 then 6 1 = 1 6 = 6

The product of any number and zero is equal to zero.


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MultiplicativeInverse Property

Two numbers whose product is 1 are called multiplicative

inverses or reciprocals.

Zero has no reciprocal because any number times 0 is 0.

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Equality Properties allow you to compute with expressions on both sides of anequation by performing identical operations on both sides of the equation. Thiscreates a balance to the mathematical problem and allows you to keep the equationtrue and thus be referred to as a property. The basic rules to solving equations isbased on these properties. Whatever you do to one side of an equation; You mustperform the same operation(s) with the same number or expression on the otherside of the equals sign.

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Substitution Property of Equality

Addition Property of Equality


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Reflexive Propertyof Equality

For any number a, a = a.

If a = a ; then 7 = 7;

then 5.2 = 5.2

The reflexive property of equality says that any real number isequal to itself.

Many mathematical statements and algebraic properties arewritten in if-thenform when describing the rule(s) or giving anexample.

The hypothesis is the part following if, and the conclusion isthe part following then.


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Symmetric Propertyof Equality

For any numbers a and b, if a = b, then b = a.

If 10 = 7 + 3; then 7 +3 = 10

If a = b then b = a

The symmetric property of equality says that if one quantityequals a second quantity, then the second quantity alsoequals the first.

Many mathematical statements and algebraic properties arewritten in if-thenform when describing the rule(s) or giving an

example.



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Transitive Propertyof Equality

For any numbers a, b and c, if a = b and

b = c, then a = c.

If 8 + 4 = 12 and 12 = 7 + 5, then 8 + 4 = 7 + 5

If a = b and b = c , then a = c

The transitive property of equality says that if one quantityequals a second quantity, and the second quantity equals athird quantity, then the first and third quantities are equal.

Many mathematical statements and algebraic properties arewritten in if-thenform when describing the rule(s) or giving an

example.



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SubstitutionProperty of Equality

If a = b, then a may be replaced by b in any

expression.

If 8 + 4 = 7 + 5; since 8 + 4 = 12 or 7 + 5 = 12;

Then we can substitute either simplificationinto the original mathematical statement.

The substitution property of equality says that a quantity maybe substituted by its equal in any expression.




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Addition Propertyof Equality

If a = b, then a + c = b + c or a c = b - c

If 6 = 6 ; then 6 +3 = 6 + 3 or 6 3 = 6 - 3

If a = b ; then a + c = b + c or a

c = b - c

The addition property of equality says that if you add orsubtract equal quantities to each side of the equation you getequal quantities.



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