Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Transcript

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.