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The Order of Operations

The Order of Operations. Algebra; Section 1.3. The Order of Operations. First do any operations that occur within grouping symbols. Then evaluate any powers, left to right if there are more than 1. Then do all multiplications and divisions, in order, left to right.

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The Order of Operations

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  1. The Order of Operations Algebra; Section 1.3

  2. The Order of Operations • First do any operations that occur within grouping symbols. • Then evaluate any powers, left to right if there are more than 1. • Then do all multiplications and divisions, in order, left to right. • Then do all additions and subtractions, in order, left to right.

  3. Grouping Symbols • Parenthesis ( ) • Brackets [ ] • Braces { } • Absolute Value | | • Fraction Bar ___ • Roots √

  4. Example 1:Evaluating Without Grouping Symbols • Evaluate the expression when x = 4. • 3x2 + 1 • 32 ÷ x2 – 1 • Solution • 3(42) + 1 = 3(16) + 1 = 48 + 1 = 49. • 32 ÷ (42) – 1 = 32 ÷ 16 – 1 = 2 – 1 = 1.

  5. Example 2:Using the Left-to-Right Rule • Evaluate the following expressions: • 24 – 8 – 6 • 15 • 2 ÷ 6 • 16 + 4 ÷ 2 – 3

  6. Example 2:Using the Left-to-Right Rule • Solution • (24 – 8) – 6 = 16 – 6 = 10 (LRR) • (15 • 2) ÷ 6 = 30 ÷ 6 = 5 (LRR) • 16 + (4 ÷ 2) – 3 = 16 + 2 – 3 (OOO) • 16 + 2 – 3 = (16 + 2) – 3 = 18 – 3 (LRR) • 18 – 3 = 15

  7. Example 3:Using a Fraction Bar • Evaluate the following: • Solution

  8. Evaluating Expressions Using a Calculator • When using a calculator to evaluate an expression it is important to remember that the calculator knows the order of operations even if you don’t. • The calculator will perform the operations in the order you tell it to, not the order you want it to.

  9. Evaluating Expressions Using a Calculator • When you enter an expression into your calculator you must enter it in such a way that the operations will get done in the correct order. • You can do this by using the parenthesis A LOT. • If you have any doubts, use parenthesis.

  10. Evaluating Expressions Using a Calculator • In order for you to enter the expression “64 + 20 ÷ 2” into your calculator correctly you must do the following: • Enter “64”, then “+”, then “(“, then “20”, then “÷”, then “2”, then “)”, then press the equals button. • The answer should be 74. • Without the parenthesis, the calculator would do 64 + 20 = 84, and then 84 ÷ 2 = 42.

  11. Evaluating Expressions Using a Calculator • If your calculator has an “expression display” screen (i.e. a screen that displays the expression as you type it in), you won’t have to worry about entering things in the correct order. • As long as you enter the expression exactly as it appears, you should be fine.

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