Section 1.4

Identity and Equality Properties

WITHOUT using any calculator or pencil/pen, evaluate the following expressions:

901 + 0 0 + 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.

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.

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)

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 _____

•Additive Identity Property

•Multiplicative Identity Property

•Multiplicative Identity Property of Zero

•Multiplicative Inverse Property

Additive Identity Property

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.

Multiplicative identity 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.

Multiplicative Property of Zero

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

If a = 6 then 6 0 = 0 6 = 0

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

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.

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•Equality 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.

•Reflexive Property of Equality

•Symmetric Property of Equality

•Transitive Property of Equality

•Substitution Property of Equality

Reflexive Property of 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 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.

Symmetric Property of 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 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.

Transitive Property of 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 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.

Substitution Property 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 simplification into the original mathematical statement.

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.

Classwork

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Homework

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