P= Parentheses E= Exponents M= Multiplication D= Division A= Addition S= Subtraction

Shorthand for repeated multiplication. (5)(5)(5) = 5 3  5 to the 3rd power (3)(3)(3)(3) = 3 4  3 to the 4th power

x 3 x 3 x 3 x 3 = x 10 x 10 = x 5 x 5 = x 4 x 4 = 64 (1/2) 3 1/2 x 1/2 x 1/2 = 1/8

x Parentheses Exponents Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) 2 x NO

23 2 x x 5 Parentheses x 5 Exponents Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) 2 x 4 3 x 5 NO

8 3 x (4 + 2) - 10 Parentheses 3 x Exponents Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) (4 + 2) 3 x 6 NO

(3 + 5) x 2 Parentheses x 2 Exponents x 2 Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) (3 + 5) 8 x

(7 – 5) 2 x 3 -1 Parentheses x 3 -1 Exponents x 3 -1 Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) (7 – 5) 2 4 x

17 Parentheses ÷ 3 x Exponents ÷ 3 x 8 -1 Multiplication and Division (in order from left to right) x Addition and subtraction (in order from left to right) ÷ 3 2 x ÷ 3 x (4 - 2) (4 - 2) 2 +16

1 (3 + 2 x 6) ÷ Parentheses (3 + 12) ÷ Exponents -none 15 ÷ Multiplication and Division (in order from left to right) Addition and Subtraction ( in order from left to right) (2 x 6) 15 ÷ Order of operations must be followed inside the parentheses

50 (5 - 8 ÷ 4) 2 x Parentheses (5 - 2) 2 x Exponents 3 2 x Multiplication and Division (in order from left to right) Addition and Subtraction ( in order from left to right) (8 ÷ 4) Order of operations must be followed inside the parentheses x x 5

7 x x (7 – 3 ÷ 3) x x x 3 = 14 – 12 = 2 + (7 – 1) x 2 3 = x 2 3 = x 8 = = 50

(5 + 4) – 2 2 x 4 ÷ (15 x 2) – ÷ – (16 ÷ 2) – 2 2 x 4 ÷ = 9 – 4 x 4 ÷ = 9 – 16 ÷ = 9 – = = – (8) = 104 – = = – ÷ 3 = 30 – ÷ 3 = 30 – = = 16