holt algebra 1 1-6 order of operations warm up 8/12/09
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Holt Algebra 1
1-6 Order of Operations
Warm Up 8/12/09
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
order of operations
Vocabulary
Holt Algebra 1
1-6 Order of Operations
E
M
A
D
S
(LEFT TO RIGHT)
P
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
Directions: Simplify using the Order of Operations
Copy Each Problem and EACH Step
Holt Algebra 1
1-6 Order of Operations
12 – 32 + 10 ÷ 2
12 – 32 + 10 ÷ 2
12 – 9 + 10 ÷ 2
12 – 9 + 5
8
There are no grouping symbols.
Evaluate powers. The exponent applies only to the 3.Divide.Subtract and add from left to right.
Example 1
Holt Algebra 1
1-6 Order of Operations
8 ÷ · 3
There are no groupingsymbols.
Divide.
48 Multiply.
Example 2
1 2
8 ÷ · 3 1 2
16 · 3
Holt Algebra 1
1-6 Order of Operations
5.4 – 32 + 6.2
5.4 – 32 + 6.2 There are no groupingsymbols.
5.4 – 9 + 6.2 Simplify powers.
–3.6 + 6.2
2.6
Subtract
Add.
Example 3
Holt Algebra 1
1-6 Order of Operations
–20 ÷ [–2(4 + 1)]
–20 ÷ [–2(4 + 1)] There are two sets of groupingsymbols.
–20 ÷ [–2(5)] Perform the operations in theinnermost set.
–20 ÷ –10
2
Perform the operation insidethe brackets.
Divide.
Example 4
Holt Algebra 1
1-6 Order of Operations
Directions: Evaluate each Expression Using the Order of
Operations
Copy each problem and each step.
Holt Algebra 1
1-6 Order of Operations
Example 5
10 – x · 6 for x = 3
10 – x · 6
10 – 3 · 6
10 – 18
–8
First substitute 3 for x.
Multiply.
Subtract.
Holt Algebra 1
1-6 Order of Operations
42(x + 3) for x = –2
42(x + 3)
42(–2 + 3)
42(1)
16(1)
16
First substitute –2 for x.
Perform the operation inside the parentheses.
Evaluate powers.
Multiply.
Example 6
Holt Algebra 1
1-6 Order of Operations
14 + x2 ÷ 4 for x = 2
Example 7
14 + x2 ÷ 4
14 + 22 ÷ 4
14 + 4 ÷ 4
14 + 1
First substitute 2 for x.
Square 2.
Divide.
Add.15
Holt Algebra 1
1-6 Order of Operations
(x · 22) ÷ (2 + 6) for x = 6
Example 8
(x · 22) ÷ (2 + 6)
(6 · 22) ÷ (2 + 6)
(6 · 4) ÷ (2 + 6)
(24) ÷ (8)
3
First substitute 6 for x.
Square two.
Perform the operations inside the parentheses.
Divide.
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
2(–4) + 22 42 – 9 –8 + 22 42 – 9
–8 + 22 16 – 9
14 7
2
Example 9
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 10
Simplify.5 + 2(–8)
(–2) – 3 3
5 + 2(–8)
–8 – 3
5 + 2(–8)
(–2) – 3 3
5 + (–16)
– 8 – 3
–11–11
1
The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing.
Evaluate the power in the denominator.
Multiply to simplify the numerator.
Add.
Divide.
Holt Algebra 1
1-6 Order of Operations
Translate From Words To Math
Copy each problem and solution.
Holt Algebra 1
1-6 Order of Operations
Example 11The quotient of -2 and the sum of -4 and x
Use parentheses to show that
the sum of -4 and x is
evaluated first.
2
( 4 )x
Holt Algebra 1
1-6 Order of Operations
Example 12
The product of 6.2 and the sum of 9.4 and 8.
6.2(9.4 + 8)Use parentheses to show that
the sum of 9.4 and 8 is
evaluated first.
Holt Algebra 1
1-6 Order of Operations
Lesson Summary
Simply each expression.
1. 2[5 ÷ (–6 – 4)] 2. 52 – (5 + 4)
|4 – 8|3. 5 8 – 4 + 16 ÷ 22
–1 4
40
Translate each word phrase into a numerical or algebraic expression.
4. 3 three times the sum of –5 and n 3(–5 + n)
5. the quotient of the difference of 34 and 9 and the square root of 25