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Rules for arithmetic and algebra expressions that describe what sequence to follow to evaluate an expression involving more than one operation. Step 1: First perform operations that are within grouping symbols such as parenthesis (), brackets [], and braces {}, and as indicated by fraction bars.Parenthesis within parenthesis are called nested parenthesis (( )). Step 2: Evaluate Powers (exponents) or roots. Step 3: Perform multiplication or division operations in order by reading the problem from left to right. Step 4: Perform addition or subtraction operations in order by Performing operations left to right only 21 6 3 5 21 6 3 5 27 3 5 27 3 5 9 5 45 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. Performing operations using order of operations 21 6 3 5 21 6 3 5 21 2 5 21 2 5 21 10 31 Can you imagine what it would be like if calculations were performed differently by various financial institutions or what if doctors prescribed different doses of medicine using the same formulas and achieving different results? 54 6 18 2 54 6 18 2 Follow the left to right rule: First solve any multiplication or division parts left to right. Then solve any addition or subtraction parts left to right. Divide 9 18 2 Multiply A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s). 9 36 45 Add The order of operations must be followed each time you rewrite the expression. 25 6 2 25 6 2 Follow the left to right rule: First solve exponent/(powers). Second solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right. Exponents (powers) 2 25 6 Multiply 50 6 A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s). Subtract 44 The order of operations must be followed each time you rewrite the expression. 3 42 8 2 Grouping 3 4 8 2 symbols 2 Follow the left to right rule: First solve parts inside grouping symbols according to the order of operations. Solve any exponent/(Powers). Then solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right. Subtract 3 4 6 2 3 16 6 48 6 8 Exponents (powers) Multiply Divide A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s). The order of operations must be followed each time you rewrite the expression. A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s). 3 42 2 (18 4) 3 4 2 (18 4) 2 3 42 Work above the fraction bar Work below the fraction bar Follow the left to right rule: Follow the order of operations by working to solve the problem above the fraction bar. Then follow the order of operations by working to solve the problem below the fraction bar. Finally, recall that fractions are also division problems – simplify the fraction. Exponents (powers) 316 48 2 (18 4) Multiply Grouping symbols 2 (18 4) 2 (14) Subtract Add Simplify: Divide The order of operations must be followed each time you rewrite the expression. 48 16 4816 3 A good habit to develop while learning order of operations is to underline the parts of the expression that you want to solve first. Then rewrite the expression in order from left to right and solve the underlined part(s). Evaluate when x=2, y=3, and n=4 ( x y 5) n 6 3 2 Substitute in the values for the variables Grouping symbols Follow the left to right rule: First solve parts inside grouping symbols according to the order of operations. Solve any exponent/(Powers). Then solve multiplication or division parts left to right. Then solve any addition or subtraction parts left to right. ( x y 3 5) n 2 6 Exponents (powers) 33 = (3)(3)(3) = 27 The order of operations must be followed each time you rewrite the expression. Add: 2 + 27 (2 33 5) 42 6 (2 27 5) 42 6 Subtract 29 - 5 (29 5) 42 6 Exponents (powers) 62 = (6)(6) = 36 24 4 2 6 Subtract 24 - 16 24 16 6 Add 86 14