Order of Operations -
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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
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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. - PowerPoint PPT Presentation
Transcript of Order of Operations -
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.
53621 ×÷+ 53621 ×÷+53621 ×÷+
5327 ×÷
59×45=
53621 ×÷+5221 ×+5221 ×+
1021+31=
5327 ×÷
#1 does each step left to right: #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.
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.
Order of Operations - WHY?
Imagine if two different people wanted to evaluate the same expression two different ways...
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?
218654 ×+÷
218654 ×+÷
2189 ×+
369 +The order of operations must be followed each time you rewrite the expression.
The order of operations must be followed each time you rewrite the expression.
45=
Divide.Divide.
Multiply.Multiply.
Add.Add.
Order of Operations: Example 1Evaluate without grouping symbols
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.
652 2 −•
652 2 −•
6252 −•
650 −
44=
Exponents (powers)Exponents (powers)
Multiply.Multiply.
Subtract.Subtract. The order of operations must be followed each time you rewrite the expression.
The order of operations must be followed each time you rewrite the expression.
Order of Operations: Example 2Expressions with powers
• Firs,t solve exponents (powers).
• Second, solve multiplication or division parts left to right.
• Then, solve any addition or subtraction parts left to right.
Exponents (powers)Exponents (powers)
Multiply.Multiply.
Subtract.Subtract.
The order of operations must be followed each time you rewrite the expression.
The order of operations must be followed each time you rewrite the expression.
( )2843 2 −÷•
( )2843 2 −÷•
Grouping symbols
Grouping symbols
( )643 2 ֥
( )6163 ֥
( )648 ÷
8=Divide.Divide.
Order of Operations: Example 3Evaluate with grouping symbols
• 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.
Exponents (powers)Exponents (powers) Multiply.Multiply.
)418(2
43 2
−+•
Work above the fraction bar.
Work above the fraction bar.
3=
Simplify: Divide.
Simplify: Divide.
243• 163•
)418(2 −+Work below the fraction bar.
Work below the fraction bar.
Grouping symbolsGrouping symbols
)14(2 +
Add.Add.
1648÷
Order of Operations: Example 4Expressions with fraction bars
4816
Exponents (powers)Exponents (powers)
Subtract.Subtract.
The order of operations
must be followed each
time you rewrite the expression.
The order of operations
must be followed each
time you rewrite the expression.
6)5( 23 +−−+ nyx
Add.Add.
Evaluate when x=2, y=3, and n=4:
64)532( 23 +−−+1) Substitute in the values for the variables1) Substitute in the values for the variables
64)5272( 2 +−−+
64)529( 2 +−−
Exponents (powers)Exponents (powers) 6424 2 +−
61624 +−
68+ 14=Subtract.Subtract.
Add.Add.
Order of Operations: Example 5Evaluate variable expressions
Inside grouping symbols:
Inside grouping symbols:
Continue with the
rest:
Continue with the
rest:
