1-4 Identity and Equality Properties The properties need to be memorized and understood. Algebra 1 Glencoe McGraw-Hill Linda Stamper

Identity Property Additive Identity: The sum of a number and 0 is the number. Thus, 0 is called the additive identity. 16 + 0 = 16 n + 0 = n Multiplicative Identity: The product of any number and 1 is the number. Thus, 1 is called the multiplicative identity. 16 • 1 = 16 n • 1 = n

When two signs are needed use parentheses or a superscript! Inverse Property Additive Inverses: Two numbers with a sum of zero are called additive inverses. Multiplicative Inverses: Two numbers whose product is 1 are called multiplicative inverses or reciprocals. When two signs are needed use parentheses or a superscript!

Zero Zero has no reciprocal because any number times 0 is 0. Multiplicative Property of Zero: The product of any number and 0 is equal to zero.

Equality Properties Reflexive: Any quantity is equal to itself. 3 = 3 5 + 2 = 5 + 2 n = n Symmetric: If one quantity equals a second quantity, then the second quantity is equal to the first. If 16 + 4 = 20 , then 20 = 16 + 4. If a = b, then b = a.

Equality Properties Transitive: If one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity. If 5 + 4 = 6 + 3 and 6 + 3 = 9 , then 5 + 4 = 9. If a = b and b = c, then a = c. Substitution: A quantity may be substituted for its equal in any expression. If n = 4, then 5n = 5(4). If a = b, then 3a = 3b.

Multiplicative Identity Find the value of n in each equation. Then name the property that is used. Given Multiplicative Identity because 42 • 1 = 42 Given Multiplicative Inverse (Reciprocal)

Find the value of n in each equation Find the value of n in each equation. Then name the property that is used. Example 1 7 = 7 + n Given n = 0 Additive Identity because 7 + 0 = 7 Example 2 9 - n = 0 Given n = 9 Additive Inverse because 9 - 9 = 0

Copy in your spiral notebook! The properties of identity and equality can be used to justify each step when evaluating expressions. Evaluate. Name the property used in each step. Given Substitution Substitution Multiplicative Identity Multiplicative Inverse Substitution Copy in your spiral notebook!

Evaluate. Name the property used in each step. Example 3 Example 4

Example 3 Evaluate. Name the property used in each step. Given Substitution Substitution Substitution Multiplicative Inverse Multiplicative Identity Substitution

Example 4 Evaluate. Name the property used in each step. Given Multiplicative Inverse Substitution Multiplicative Identity Substitution

Homework 1-A6 Pages 23-25 #8-23,26-28,40-41,46.