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Order of Operations rules for arithmetic and algebra that describe what sequence to follow to evaluate an expression involving more than one operation The Rules Step 1: Do operations inside grouping symbols such as parentheses (), brackets [], and braces {}, and operations separated by fraction bars. Parentheses within parentheses are called nested parentheses (( )). Step 2: Evaluate Powers (exponents) or roots. Step 3: Perform multiplication or division in order by reading the problem from left to right. Step 4: Perform addition or subtraction in order by reading the problem from left to right. Order of Operations - WHY? Imagine if two different people wanted to evaluate the same expression two different ways... #1 does each step left to right: 21 6 3 5 21 6 3 5 27 3 5 27 3 5 9 5 45 #2 uses the order of operations The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results. Method 2 is the correct method. 21 6 3 5 21 6 3 5 21 2 5 21 2 5 21 10 31 Order of Operations - WHY? • Can you imagine what it would be like if calculations were performed differently by various financial institutions? • What if doctors prescribed different doses of medicine using the same formulas but achieving different results? Order of Operations: Example 1 Evaluate without grouping symbols 54 6 18 2 54 6 18 2 Divide. 9 18 2 This expression has no parentheses and no exponents. • First solve any multiplication or division parts left to right. • Then solve any addition or subtraction parts left to right. Multiply. 9 36 45 Add. The order of operations must be followed each time you rewrite the expression. Order of Operations: Example 2 Expressions with powers 25 6 • Firs,t solve exponents (powers). 25 6 • Second, solve multiplication or division parts left to right. 2 2 Exponents (powers) 2 25 6 Multiply. • Then, solve any addition or subtraction parts left to right. 50 6 Subtract. 44 The order of operations must be followed each time you rewrite the expression. Order of Operations: Example 3 Evaluate with grouping symbols 3 4 8 2 • First, solve parts inside grouping symbols according to the order of operations. 2 3 42 8 2 3 42 6 3 16 6 48 6 8 Grouping symbols • Solve any exponent (Powers). Subtract. Exponents (powers) Multiply. Divide. • Then, solve multiplication or division parts left to right. • Then solve any addition or subtraction parts left to right. The order of operations must be followed each time you rewrite the expression. Order of Operations: Example 4 Expressions with fraction bars Work above the fraction bar. 3 4 2 (18 4) 2 Work below the fraction bar. Exponents (powers) 3 4 2 2 (18 4) Grouping symbols Multiply. 316 2 (14) Add. 48 16 Simplify : Divide. 4816 3 Order of Operations: Example 5 Evaluate variable expressions ( x y 5) n Evaluate when x=2, y=3, and n=4: 1) Substitute in the values for the variables 3 Inside grouping symbols: 6 Exponents (powers) (2 33 5) 42 6 Add. (2 27 5) 42 6 Subtract. Continue with the rest: 2 (29 5) 42 6 Exponents (powers) 24 4 2 6 Subtract. 24 16 6 Add. 86 14 The order of operations must be followed each time you rewrite the expression.