Order of Operations

1
Algebra 1 Section 1.4 Order of Operations
Order of Operations

• WORK INSIDE Parentheses or brackets
• Evaluate any exponents
• Multiply and Divide from left to right
• Add and subtract from left to right
• start over at 2 inside parentheses or brackets

1. 4 2 1 6 1 (add 4 2) 5

• 8 2 3
• 16 3 (multiply 8 2)
• 13

• 6 2 4 3
• 3 4 3 (Divide 6 by 2)
• 3 12 (multiply 4 by 3)
• 15

• 24 4 52
• 24 4 25 (Simplify 52)
• 6 25 (Simplify 24 4)
• 31

2
5. 30 (4 3 2) 30 (4 6) (simplify 3
2 inside parentheses) 30 (10) (simplify
4 6 inside parentheses) 3

• 8 32 7 4 1
• 8 9 7 4 1 (simplify 32)

72 28 1 (simplify 8 9 and also 7 4)
44 1 (simplify 72 28) 45

• 82 42(3) 2
• 82 46 2 (multiply 2(3) inside
  brackets)
• 82 4(8) (add 6 2 inside brackets)
• 64 4(8) (simplify 82)
• 64 32 (multiply 4(8))
• 96

These 2 steps could be combined into 1
3
8. 3 4 2 6 5(2 1) 42 8 2 22
4 0 3 4 2 6 5(3) 42 8 2 22
4 0 (parentheses 1st) 3 4 2 6
5(3) 16 8 2 4 4 0 (exponents
2nd) 3 8 6 15 16 4 4 4 0
(multiply and divide 3rd) 0
Evaluate the expression
10. x3 4x 7, when x 3 33 4(3) 7
(substitute) 27 4(3) 7 (exponent)
27 12 7 (multiply) 8

• 3 2x3, when x 2
• 3 2(2)3 (substitute 2 for x)
• 3 2(8) (simplify 23)
• 3 16 (simplify 2(8))
• 19

4

• 3x2 2y
• 2 , when x 2 and y 4
• 3(2)2 2(4) (substitute)
• 2
• 3(4) 8 (simplify both 22 and 2(4),
  since they
• 2 do not affect each other)
• 12 8 (multiply 3(4))
• 2
• 4 (simplify 12 8)
• 2
• 2

5

• Write an expression for the perimeter of the
  triangle.
• Then use the expression to find the perimeter
  when x 3.2 ft

4x
2x
3x
Perimeter 2x 3x 4x 9x
If x 3.2, then 9x 9(3.2) 28.8 ft