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

3. 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

4. 3535 4343 10 3 5353 3 x 3 x 3 x 3 x 3 = 243 10 x 10 x 10 = 1000 5 x 5 x 5 = 125 4 x 4 x 4 = 64 (1/2) 3 1/2 x 1/2 x 1/2 = 1/8

5. 3 1 + 2 x 3 - 4 Parentheses 1 + 6 - 4 Exponents 7 - 4 Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) 2 x 3 1 + 6 NO

6. 23 2 x 4 + 3 x 5 Parentheses 8 + 3 x 5 Exponents 8 + 15 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

7. 8 3 x (4 + 2) - 10 Parentheses 3 x 6 - 10 Exponents 18 - 10 Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) (4 + 2) 3 x 6 NO

8. 20 2 2 + (3 + 5) x 2 Parentheses 2 2 + 8 x 2 Exponents 4 + 8 x 2 Multiplication and Division (in order from left to right) Addition and subtraction (in order from left to right) (3 + 5) 8 x 2 2 4 + 16

9. 13 2 + (7 – 5) 2 x 3 -1 Parentheses 2 + 2 2 x 3 -1 Exponents 2 + 4 x 3 -1 Multiplication and Division (in order from left to right) 2 + 12 -1 14 -1 Addition and subtraction (in order from left to right) (7 – 5) 2 4 x 3 2 + 12 14 -1

10. 17 Parentheses 2 + 6 ÷ 3 x 2 3 -1 Exponents 2 + 6 ÷ 3 x 8 -1 Multiplication and Division (in order from left to right) 2 + 2 x 8 -1 2 +16 -1 Addition and subtraction (in order from left to right) 2323 6 ÷ 3 2 x 8 18 -1 2 + 6 ÷ 3 x (4 - 2) 3 - 1 (4 - 2) 2 +16

11. 1 (3 + 2 x 6) ÷ 5 - 2 Parentheses (3 + 12) ÷ 5 - 2 Exponents -none 15 ÷ 5 - 2 Multiplication and Division (in order from left to right) Addition and Subtraction ( in order from left to right) (2 x 6) 15 ÷ 5 3 - 2 Order of operations must be followed inside the parentheses 3 + 12 3 - 2

12. 50 (5 - 8 ÷ 4) 2 x 5 + 5 Parentheses (5 - 2) 2 x 5 + 5 Exponents 3 2 x 5 + 5 Multiplication and Division (in order from left to right) Addition and Subtraction ( in order from left to right) (8 ÷ 4) 45 + 5 Order of operations must be followed inside the parentheses 5 - 2 45 + 5 3232 9 x 5 + 59 x 5

13. 7 x 2 - 2 2 x 3 2 2 + (7 – 3 ÷ 3) x 2 3 7 x 2 - 4 x 3 = 14 – 12 = 2 + (7 – 1) x 2 3 = 2 + 6 x 2 3 = 2 + 6 x 8 = 2 + 48 = 50

14. (5 + 4) – 2 2 x 4 ÷ 2 + 6 (15 x 2) – 4 2 + 6 ÷ 3 104 – (16 ÷ 2) 2 + 10 9 – 2 2 x 4 ÷ 2 + 6 = 9 – 4 x 4 ÷ 2 + 6 = 9 – 16 ÷ 2 + 6 = 9 – 8 + 6 = 1 + 6 = 7 104 – (8) 2 + 10 = 104 – 64 + 10= 40 + 10 = 50 30 – 4 2 + 6 ÷ 3 = 30 – 16 + 6 ÷ 3 = 30 – 16 + 2 = 14 + 2 = 16