Algebra 1 Section 1.8

Order of Operations It is very important that mathematicians agree on the order with which numeric expressions are calculated!

Order of Operations Evaluate within innermost grouping symbols first. Evaluate all exponential expressions.

Order of Operations 3. Perform all multiplication and division from left to right 4. Perform all addition and subtraction from left to right

Example 1 2 + 32 – 4 ÷ 2 • 3 2 + 9 – 4 ÷ 2 • 3 2 + 9 – 2 • 3 2 + 9 – 6 5

Example 1 b. 23 – 12 + 5 • 4 – 32 + 9 ÷ 3 23 – 12 + 5 • 4 – 32 + 9 ÷ 3 8 – 1 + 5 • 4 – 9 + 9 ÷ 3 8 – 1 + 20 – 9 + 3 21

Grouping Symbols These indicate which operations to perform first Parentheses ( ) Brackets [ ] Braces { }

Grouping Symbols These indicate which operations to perform first Absolute value symbols, the fraction bar, and the radical sign are also used as grouping symbols

Grouping Symbols These indicate which operations to perform first If grouping symbols are within other grouping symbols, the operations inside the innermost grouping symbols must be done first

Example 2 2 + 3(5 + 7) ÷ 2 2 + 3(12) ÷ 2 2 + 36 ÷ 2 2 + 18 20

Example 2 b. 2(-3 + 7) – (7 – 5) 5 – 3(1 – 4) 2(4) – 2 5 – 3(-3) 8 – 2 5 + 9 6 14 = 3 7 =

Example 2 c. 9 – 3|2 + 7 • 23(3 – 5)| – 4 9 – 3|2 + 7 • 23(-2)| – 4 9 – 3|2 + 7 • 8(-2)| – 4 9 – 3|2 – 112| – 4 9 – 3|-110| – 4 9 – 3(110) – 4

Example 2 9 – 3(110) – 4 9 – 330 – 4 -325

Homework: pp. 36-37