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  5. Is the total cost $100 or $300 ? In the Real World Order of Operations 1 4.

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  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.

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.

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

Order of Operations Evaluate x – 3y 3 when x = 25 and y = 2. Evaluating a Variable Expression EXAMPLE 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

Order of Operations Using the Left-to-Right Rule EXAMPLE 3 Subtract 7 from 12. Add 5 and 3. Subtract 6 from – – 6 = – 68 = = 12 – – 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.

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 – – 6 = – 68 = 2 54 ÷ 9 ÷ 3 = = 12 – – 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.

Order of Operations —––– = Using Grouping Symbols EXAMPLE 4 —––– Add 13 and 7. Multiply 2 and 5. Divide 20 by 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.

Order of Operations —––– = Using Grouping Symbols EXAMPLE 4 —––– Add 13 and 7. Multiply 2 and 5. Divide 20 by 10. = 2 (4 + 1) 2 3 Add inside parentheses. Evaluate the power. = Multiply 25 and 3. = = (4 + 1) 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.