: Algebra I Order of Operations
: Goal 1: Using the Order of Operations Mathematicians have established an order of operations to evaluate an expression involving more than one operation. Start with operations within grouping symbols. Then evaluate powers. Then do multiplications and divisions from left to right. Finally, do additions and subtractions from left to right.
: Evaluating Without Grouping Symbols Evaluate the expression when x = 4. a. 3x^2 + 1 = 3 * 4^2 + 1 Substitute 4 for x. = 3(16) + 1 Evaluate power. = 48 + 1 Evaluate product. = 49 Evaluate sum. b. 32/x^2 - 1 = 32/4^2 - 1 Substitute 4 for x. = 32/16 - 1 Evaluate power. = 2 - 1 Evaluate quotient. = 1 Evaluate difference.
: Reminder and the Left-To-Right Rule - When you want to change the established order of operations for an expression, you must use parentheses or other grouping symbols. The Left-To-Right Rule: Operations that have the same priority, such as multiplication and division or addition and subtraction, are performed using the left-to-right rule.
: Using the Left-To-Right Rule a. 24 - 8 - 6 = (24 - 8) - 6 Work from left to right. = 16 - 6 = 10 b. 15(2)/6 = (15 * 2)/6 Work from left to right. = 30/6 = 5 c. 16 + 4/2 - 3 = 16 + (4/2) - 3 Divide first. = 16 + 2 - 3 = (16 + 2) - 3 Work from left to right. = 18 - 3 = 15
: Order of Operations First do operations that occur within grouping symbols.
Then evaluate powers.
Then do multiplications and divisions from left to right.
Finally, do additions and subtractions from left to right.
: Another Reminder A fraction bar can act as a grouping symbol: (1 + 2)/(4 - 1) = 1 + 2 ------- 4 - 1.
: Using a Fraction Bar 7(4)---------------8 + 7^2 - 1 = 7(4)-------------8 + 49 - 1 Evaluate power.
: Using a Fraction Bar Con. 28------------ Simplify the numerator.8 + 49 - 1 28----------- Work from left to right. 57 - 1 28------ Subtract. 1 56 -------- Simplify. 2
: Goal 2: Evaluating Expressions With A Calculator Many calculators use the established order of operations, but some do not. See if your calculator uses the established order of operations in the next example. If your calculator does not follow the order of operations, you must enter the operations in the correct order.
: Using A Calculator When you enter the following in your calculator, does the calculator display 6.1 or 0.6? 10.5 - 6.3/2.1 - 1.4 Enter If your calculator uses order of operations, it will display 6.1. 10.5 - 6.3/2.1 - 1.4 = 10.5 - (6.3/2.1) - 1.4 = 10.5 - 3 - 1.4 = 6.1b. If it displays 0.6, it performs the operations as they are entered. [(10.5 - 6.3)/2.1] - 1.4 = (4.2/2.1) - 1.4 = 2 - 1.4 = 0.6
: Calculating Sales Tax Suppose you live in a state that charges no sales tax on essentials, such as clothes or food, but charges 6% sales tax on nonessentials, such as CDs or games. You decide to buy a sweatshirt for $24 and a video game for $39. Your calculator follows the established order of operations. Which of the following keystroke sequences will show the correct amount you owe? Explain why.
: Calculating Sales Tax Con. a. 24 + 39 + 39(0.06) ENTER b. 39 + 24 + 24(0.06) ENTER c. 39 + 24(24 + 39) * 0.06 ENTER Tell which and explain why please.
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