Presentation on theme: "Properties of Numbers; Operations with Integers Presented by Mr. Laws 8 th Grade Math, JCMS."— Presentation transcript:
Properties of Numbers; Operations with Integers Presented by Mr. Laws 8 th Grade Math, JCMS
Essential Question: How can the operations of integers and algebraic expressions be associated to the properties of numbers?
Properties of Numbers Commutative Property a + b = b + a a x b = b x a 8 +2 = 2 + 8 6 x 4 = 4 x 6 Associative Property a + (b + c) = (a + b) +c a x (b x c) = (a x b) x c 2 + (4+6) = (2 + 4) + 6 5 x (6 x 4) = (5 x 6) x 4 Distributive Property a(b + c) = ab + ac a(b – c) = ab - ac 3 (2 + 4) = 3(2) + 3(4) 3 (6 – 2) = 3(6) – 3 (2) Identity Propertya + 0 = a a x 1 = a 4 + 0 = 4 5 x 1 = 5
Algebraic Expression What is a algebraic expression? It contains a variable, a number and at least one operation symbol. n + 5 or 5 – x When you evaluate an expression, you are finding the numerical value.
Orders of Operation What is the orders of operation? A familiar acronym: Please Excuse My Dear Aunt Sally In Math we call it PEMDAS 1.Parenthesis 2.Exponents 3.Multiplications 4.Division 5.Addition 6.Subtraction.
Key Ideas to Remember Do all operations within grouping symbol first; start with the innermost grouping symbols. Evaluate all powers before other operations. Multiply and divide in order from left to right. Add and subtract in order from left to right.
For example Evaluate the following expression.
Evaluate Algebraic Expressions Sometimes you will have to evaluate algebraic expression: Example: Evaluate each expression if a=5, b=4, and c=8.
Absolute Value The absolute value of a number is the distance the number is from 0. The absolute value of a number is always positive or zero. For Example: Both absolute values are 4 units away from zero.
Absolute Value Expressions Evaluate each expression: Evaluate ea. expression if a= -5 and b = 3.
Questions and Review Write at least four questions pertaining to this lesson. What did you learn in the lesson? What do you still need to learn in this lesson? What are some important things to remember about this lesson?