Week 1 Real Numbers and Their Properties Section

Week 1 Real Numbers and Their Properties (Section 1. 5: Exponential Expressions and the Order of Operations)

Week 1 Objectives This week students will: • Utilize proper math terminology in written explanations. • Compute basic operations with signed numbers. • Exemplify properties of real numbers. • Execute simplification techniques on expressions and equations.

Exponential Expression • • An expression of the form an is known as an exponential expression. It is read as “a to the power of n” a is known as the base and n is known as the exponent. Examples: 25, (1/3)2, (-3)4…. Thus, 25 means multiply 2 five times as: 2*2*2 = 32 (1/3)2 means multiply 1/3 twice as: (1/3)*(1/3) = 1/9 (-3)4 means multiplying -3 four times as -3*-3*-3*-3 = 81 • If the power is 1, then we do not write the power explicitly. Thus, 21 is written as 2.

$Order of operations • We have learned about whole numbers, fractions and mixed numbers$

Order of operations • We have learned about whole numbers, fractions and mixed numbers • We have learned about various operations like addition, subtraction, multiplication and division. • When evaluating mathematical expressions involving various operations, then we follow certain order: 1. Expressions contained inside any parentheses, brackets are evaluated first 2. Exponents are evaluated 3. All the multiplications and divisions are then done, in order, starting at the left and moving right. 4. Finally, we do all additions and subtractions, from left to right.

Pemdas • The order of operations can be easily remembered through PEMDAS – Parentheses, Exponent, Multiplication, Division, Addition and Subtraction

Example 1 Simplify the expression: By PEMDAS, we need to do the multiplication first and then addition: Adding the two fractions:

Example 2 • Simplify the expression: • By PEMDAS, parenthesis first, then multiplication and last of all addition: Multiply 1/3 to 1/8: Add ½ to 1/24:

Example 3 • Simplify Step 1: Simplify the expression in the numerator and the denominator: Step 2: Since the end-result is a division, write the denominator as a reciprocal and multiply to get the final solution:

Example 4 • Simplify • Solution