Transcript Order of Operations and Exponents

Order of Operations with
Exponents and Integers
Today you will learn to:
• use the order of operations to evaluate expressions.
• evaluate expressions with exponents
• evaluate expressions with integers
M7.A.2.1.1
Warm-up Problem: Order of
Operations
Frankie orders two
hamburgers and a soda for
lunch. A hamburger is $3
and a soda is $1.00. Write
an expression to show how
much he paid for lunch.
Then find the value of the
expression.
Order of Operations
Expressions, like 1 + 5 x 6, are numerical expressions,
which contain a combination of numbers and operations (like
addition or multiplication).
When you evaluate an expression, or find it’s
numerical value, you must follow the Order of Operations:
1. Simplify the expressions inside the Parenthesis, or grouping
symbols.
2. Do all the Exponents from left to right.
3. Do all Multiplications and/or Divisions from left to right.
4. Do all Additions and/or Subtractions from left to right.
Remember: Please Excuse My Dear Aunt Sally
Order of Operations: Examples
Example 1: 3 + 4 x 5
3 + 4 x 5 = 3 + 20
Multiply 4 and 5
3 + 20 = 23
Add 3 and 20
Example 2: 6 (2 + 9) – 3 x 8
6 (2 + 9) – 3 x 8 = 6 (11) – 3 x 8
Add 2 and 9
6 (11) – 3 x 8 = 66 – 3 x 8
Multiply 6 and 11
66 – 3 x 8 = 66 - 24
Multiply 3 and 8
66 – 24 = 42
Subtract 24 from 66
Exponents
An exponent tells you how many times a
number, or base, is used as a factor. For example, if
you were given the problem 32 it would be the same as
writing 3 x 3.
Example: Rewrite and simplify the expression 55.
Example: Simplify each expression using the order of
operations:
A. 18 + 36 ÷ 32
B. 8 + (2 x 5) x 34 ÷ 9
Operations with Integers
Some numerical expressions that you will be asked
to solve may include integers. While it is important to
remember your rules for solving problems involving
integers, you will be using a calculator to solve these
problems.
Example 1: 3 + (- 4) x 5
3 + (- 4) x 5 = 3 + (- 20)
Multiply - 4 and 5
3 + (- 20) = -17
Add 3 and - 20