Holt Algebra 1
1-6 Order of Operations1-6 Order of Operations
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
1-6 Order of Operations
Find each square root.
1.
Write all classifications that apply to each real
number.
3. -55
Bell Quiz 1-6
5 pts
possible
3 pts
2 pts25
Holt Algebra 1
1-6 Order of Operations
Use the order of operations to simplify expressions.
Objective
Holt Algebra 1
1-6 Order of Operations
When a numerical or algebraic expression contains
more than one operation symbol, the order of operations tells which operation to perform first.
First:
Second:
Third:
Fourth:
Perform operations inside grouping symbols.
Evaluate powers.
Perform multiplication and division from left to right.
Perform addition and subtraction from left to right.
Order of Operations
Holt Algebra 1
1-6 Order of Operations
Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first.
Holt Algebra 1
1-6 Order of Operations
Helpful Hint
The first letter of these words can help you remember the order of operations.
Please
Excuse
My
Dear
Aunt
Sally
Parentheses
Exponents
Multiply
Divide
Add
Subtract
Holt Algebra 1
1-6 Order of Operations
Simplify each expression.
A. 15 – 2 · 3 + 1
There are no grouping symbols.
Multiply.
Subtract and add from left to right.
B. 12 – 32 + 10 ÷ 2
There are no grouping symbols.
Evaluate powers. The exponent applies only to the 3.
Divide.Subtract and add from left to right.
Example 1: Translating from Algebra to Words
Holt Algebra 1
1-6 Order of Operations
1a: 8 ÷ · 3
There are no
grouping symbols.
Divide. Multiply.
Check It Out! Example 1
Simplify each expression.1 2
1b: 5.4 – 32 + 6.2 There are no
grouping symbols.
Subtract. Add.
1c: –20 ÷ [–2(4 + 1)]There are two sets of
grouping symbols.
Perform the operations
in the innermost set.Perform the operation
inside the brackets.Divide.
Holt Algebra 1
1-6 Order of Operations
Example 2A: Evaluating Algebraic Expressions
Evaluate the expression for the given value
of x.
10 – x · 6 for x = 3
First substitute 3 for x.
Multiply.
Subtract.
Holt Algebra 1
1-6 Order of Operations
Evaluate the expression for the given value of x.
42(x + 3) for x = –2
First substitute –2 for x.
Perform the operation inside the parentheses.
Evaluate powers.
Multiply.
Example 2B: Evaluating Algebraic Expressions
Holt Algebra 1
1-6 Order of Operations
Evaluate the expression for the given value of x.
2a: 14 + x2 ÷ 4 for x = 2
2b: (x · 22) ÷ (2 + 6) for x = 6
Check It Out! Example 2
Holt Algebra 1
1-6 Order of Operations
Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division.
Holt Algebra 1
1-6 Order of Operations
Simplify.
2(–4) + 22
42 – 9
Example 3A: Simplifying Expressions with Other
Grouping Symbols
The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing.
Multiply to simplify the numerator.
Evaluate the power in the denominator.
Add to simplify the numerator. Subtract to simplify the denominator.
Divide.
Holt Algebra 1
1-6 Order of Operations
Example 3B: Simplifying Expressions with Other
Grouping Symbols
Simplify.
3|42 + 8 ÷ 2|
The absolute-value symbols act as grouping symbols.
Evaluate the power.
Divide within the absolute-value
symbols.
Add within the absolute-symbols.
Write the absolute value of 20.
Multiply.
Holt Algebra 1
1-6 Order of Operations
3a: 5 + 2(–8)
(–2) – 3
3b: |4 – 7|2 ÷ –3
Check It Out! Example 3a
Simplify.
3
Holt Algebra 1
1-6 Order of Operations
Check It Out! Example 3c
Simplify.
The radical symbol acts as a grouping symbol.
Subtract.
Take the square root of 49.
Multiply.
Holt Algebra 1
1-6 Order of Operations
You may need grouping symbols when translating from words to numerical expressions.
Remember!
Look for words that imply mathematical operations.
difference subtractsum addproduct multiply
quotient divide
Holt Algebra 1
1-6 Order of Operations
HOMEWORKSec 1-6 (Pg 43)1, 2, 5, 8, 11, 14, 17, 24-38, 42-46, 66, 81, 83, 85, 87, 88
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