Name: _________________________________________________ Period: ___________ Date: ________________ Properties of Real Numbers Guide Notes PROPERTIES OF REAL NUMBERS Let π, π, and π be any real numbers 1. IDENTITY PROPERTIES A. Additive Identity The sum of any number and π is equal to the number. Thus, π is called the additive identity. For any number π, the sum of π and π is π. B. Multiplicative Identity The product of any number and π is equal to the number. Thus, π is called the multiplicative identity. For any number π, the product of π and π is π. 2. INVERSE PROPERTIES A. Additive Inverse The sum of any number and its opposite number (its negation) is equal to π. Thus, π is called the additive inverse. For any number π, the sum of π and βπ is π. B. Multiplicative Property of Zero For any number π, the product of π and π is π. C. Multiplicative Inverse The product of any number and its reciprocal is equal to π. Thus, the numberβs reciprocal is called the multiplicative inverse. π For any number π, the product of π and its reciprocal is π. π π π π For any numbers , where π β π, the product of and its reciprocal π π π is π. Copyright © Algebra1Coach.com 1 Name: _________________________________________________ Period: ___________ Date: ________________ Properties of Real Numbers Guide Notes Sample Problem 1: Name the property in each equation. Then find the value of π. a. ππ β π = ππ b. π + π = ππ c. πβ π=π d. π + ππ = π e. πβ π=π f. π β π=π π 3. EQUALITY PROPERTIES A. Reflexive Any quantity is equal to itself. For any number π, π = π. B. Symmetric If one quantity equals a second quantity, then the second quantity equals the first quantity. For any numbers π and π, if π = π then π = π. C. Transitive If one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity. For any numbers π, π, and π, if π = π and π = π, then π = π. D. Substitution A quantity may be substituted for its equal in any expression. If π = π, then π may be replaced by π in any expression. Copyright © Algebra1Coach.com 2 Name: _________________________________________________ Period: ___________ Date: ________________ Properties of Real Numbers Guide Notes π Sample Problem 2: Evaluate π(ππ β π) + π β , if π = π and π = π. Name the property of equality used in each step. π 4. COMMUTATIVE PROPERTIES A. Addition The order in which two numbers are added does not change their sum. For any numbers π and π, π + π is equal to π + π. B. Multiplication The order in which two numbers are multiplied does not change their product. For any numbers π and π, π β π is equal to π β π. 5. ASSOCIATIVE PROPERTIES A. Addition The way three or more numbers are grouped when adding does not change their sum. For any numbers π, π, and π, (π + π ) + π is equal to π + (π + π). B. Multiplication The way three or more numbers are grouped when multiplying does not change their product. For any numbers π, π, and π, (π β π ) β π is equal to π β (π β π). Sample Problem 3: Simplify variable expressions. Show all possible answers. a. π + (π + π) b. (π + π) + π c. π β ππ d. (π + π) + π e. (π)(ππ) Copyright © Algebra1Coach.com 3
© Copyright 2026 Paperzz