1. Music You buy a used guitar for $50. You then pay $10 for each of 5 guitar lessons. The total cost can be found by evaluating the expression 50 + 10  5. Is the total cost $100 or $300 ? In the Real World Order of Operations 1 4.

2. Music You buy a used guitar for $50. You then pay $10 for each of 5 guitar lessons. The total cost can be found by evaluating the expression 50 + 10  5. Is the total cost $100 or $300 ? In the Real World So that everyone gets the same result when evaluating an expression, a set of rules called the order of operations is always followed. Order of Operations 1 4.

3. NOTE BOOK Order of Operations Evaluate expressions inside grouping symbols. Evaluate powers. Multiply and divide from left to right. Add and subtract from left to right. Order of Operations 1 4.

4. Order of Operations To find the guitar costs as described, evaluate 50 + 10  5. First multiply 10 and 5. 50 + 10  5 = 100 Following Order of Operations EXAMPLE 1 1 4. = 50 + 10  5 ANSWER The total cost is $100. Then add 50 and 50. 50

5. Order of Operations Evaluate x – 3y 3 when x = 25 and y = 2. Evaluating a Variable Expression EXAMPLE 2 1 4. x – 3y 3 Substitute 25 for x and 2 for y. Evaluate the power. = 25 – 3(2 3 ) Multiply 8 and 3. Then subtract 24 from 25. (8) = 25 – 3(8)24 SOLUTION = x – 3 y 3 (2 3)(2 3) 25 = 1= 1

6. Order of Operations Using the Left-to-Right Rule EXAMPLE 3 Subtract 7 from 12. Add 5 and 3. Subtract 6 from 8. 12 – 7 + 3 – 6 = 5 + 3 – 68 = 2 1 4. = 12 – 7 + 3 – 65 Left-to-Right Rule When an expression has a string of additions and subtractions or a string of multiplications and divisions, you need to perform the operations in order from left to right.

7. Order of Operations Using the Left-to-Right Rule EXAMPLE 3 Subtract 7 from 12. Add 5 and 3. Subtract 6 from 8. Divide 54 by 9. Divide 6 by 3. 12 – 7 + 3 – 6 = 5 + 3 – 68 = 2 54 ÷ 9 ÷ 3 = 2 1 4. = 12 – 7 + 3 – 65 = 54 ÷ 9 ÷ 3 6 Left-to-Right Rule When an expression has a string of additions and subtractions or a string of multiplications and divisions, you need to perform the operations in order from left to right.

8. Order of Operations —––– 13 + 7 2 5 = Using Grouping Symbols EXAMPLE 4 —––– 13 + 7 2 5 Add 13 and 7. Multiply 2 and 5. Divide 20 by 10. = 2 1 4. 20 10 Grouping Symbols Grouping symbols indicate operations that should be performed first. The most common grouping symbols are parentheses ( ) and brackets [ ]. A fraction bar is also a grouping symbol.

9. Order of Operations —––– 13 + 7 2 5 = Using Grouping Symbols EXAMPLE 4 —––– 13 + 7 2 5 Add 13 and 7. Multiply 2 and 5. Divide 20 by 10. = 2 (4 + 1) 2 3 Add inside parentheses. Evaluate the power. = 5 2 3 25 Multiply 25 and 3. = 75 1 4. 20 10 = (4 + 1) 2 3 5 2 Grouping Symbols Grouping symbols indicate operations that should be performed first. The most common grouping symbols are parentheses ( ) and brackets [ ]. A fraction bar is also a grouping symbol.