1. 1-6 Order of Operations Warm Up Lesson Presentation Lesson Quiz
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1

2. Warm Up Simplify. 1. 42 2. |5 – 16| 3. –23 4. |3 – 7| 16 11 –8 4
|5 – 16| – |3 – 7| 16 11 –8 4
Translate each word phrase into a numerical or algebraic expression.
5. the product of 8 and 6
8  6
6. the difference of 10y and 4
10y – 4
Simplify each fraction. 16 2 8 56 1 7 7. 8. 8

3. Objective
Use the order of operations to simplify expressions.

4. Vocabulary
order of operations

5. When a numerical or algebraic expression contains
more than one operation symbol, the order of
operations tells which operation to perform first.
Order of Operations
Perform operations inside grouping
symbols.
First:
Second:
Simplify powers and roots.
Third:
Perform multiplication and division
from left to right.
Perform addition and subtraction from
left to right.
Fourth:

6. Grouping symbols include parentheses ( ), brackets [ ], and braces { }
Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, simplify the expression inside the innermost set first. Follow the order of operations within that set of grouping symbols and then work outward.

7. 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

8. Example 1: Translating from Algebra to Words
Simplify each expression.
A. 15 – 2 · 3 + 1
15 – 2 · 3 + 1
There are no grouping symbols.
15 – 6 + 1
Multiply. 10
Subtract and add from left to right.
B. 12 – ÷ 2
12 – ÷ 2
There are no grouping symbols.
12 – ÷ 2
Evaluate powers. The exponent applies only to the 3.
12 – 9 + 5
Divide.
Subtract and add from left to
right. 8

9. Simplify the expression.
Check It Out! Example 1a
Simplify the expression.
1 2
8 ÷ · 3
8 ÷ · 3
1 2
There are no grouping
symbols.
16 · 3
Divide. 48
Multiply.

10. Check It Out! Example 1b
Simplify the expression.
5.4 –
There are no grouping
symbols.
5.4 –
5.4 –
Simplify powers. –
Subtract
2.6
Add.

11. Check It Out! Example 1c
Simplify the expression.
–20 ÷ [–2(4 + 1)]
There are two sets of grouping
symbols.
–20 ÷ [–2(4 + 1)]
Perform the operations in the
innermost set.
–20 ÷ [–2(5)]
Perform the operation inside
the brackets.
–20 ÷ –10 2
Divide.

12. Example 2A: Evaluating Algebraic Expressions
Evaluate the expression for the given value
of x.
10 – x · 6 for x = 3
10 – x · 6
First substitute 3 for x.
10 – 3 · 6
Multiply.
10 – 18
Subtract. –8

13. Example 2B: Evaluating Algebraic Expressions
Evaluate the expression for the given value of x.
42(x + 3) for x = –2
42(x + 3)
First substitute –2 for x.
42(–2 + 3)
Perform the operation inside the parentheses.
42(1)
16(1)
Evaluate powers. 16
Multiply.

14. Check It Out! Example 2a
Evaluate the expression for the given value of x.
14 + x2 ÷ 4 for x = 2
14 + x2 ÷ 4
÷ 4
First substitute 2 for x.
÷ 4
Square 2.
14 + 1
Divide. 15
Add.

15. Check It Out! Example 2b
Evaluate the expression for the given value of x.
(x · 22) ÷ (2 + 6) for x = 6
(x · 22) ÷ (2 + 6)
(6 · 22) ÷ (2 + 6)
First substitute 6 for x.
(6 · 4) ÷ (2 + 6)
Square two.
(24) ÷ (8)
Perform the operations inside the parentheses. 3
Divide.

16. Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division.

17. Example 3A: Simplifying Expressions with Other Grouping Symbols
2(–4) + 22
42 – 9
The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing.
2(–4) + 22
42 – 9
–8 + 22
42 – 9
Multiply to simplify the numerator.
–8 + 22
16 – 9
Evaluate the power in the denominator.
Add to simplify the numerator. Subtract to simplify the denominator. 14 7 2
Divide.

18. Example 3B: Simplifying Expressions with Other Grouping Symbols
3| ÷ 2|
The absolute-value symbols act as grouping symbols.
3| ÷ 2|
Evaluate the power.
3| ÷ 2|
Divide within the absolute-value symbols.
3|16 + 4|
3|20|
Add within the absolute-symbols.
3 · 20
Write the absolute value of 20. 60
Multiply.

19. Evaluate the power in the denominator.
Check It Out! Example 3a
Simplify.
5 + 2(–8)
(–2) – 3 3
The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing.
5 + 2(–8)
(–2) – 3 3
5 + 2(–8)
–8 – 3
Evaluate the power in the denominator.
5 + (–16)
– 8 – 3
Multiply to simplify the numerator.
–11
Add. 1
Divide.

20. Check It Out! Example 3b
Simplify.
|4 – 7|2 ÷ –3
The absolute-value symbols act as grouping symbols.
|4 – 7|2 ÷ –3
|–3|2 ÷ –3
Subtract within the absolute-value symbols.
32 ÷ –3
Write the absolute value of –3.
9 ÷ –3
Square 3. –3
Divide.

21. Check It Out! Example 3c
Simplify.
The radical symbol acts as a grouping symbol.
Subtract.
3 · 7
Take the square root of 49. 21
Multiply.

22. You may need grouping symbols when translating from words to numerical expressions.
Remember!
Look for words that imply mathematical operations.
difference subtract
sum add
product multiply
quotient divide

23. Example 4: Translating from Words to Math
Translate each word phrase into a numerical or algebraic expression.
A. the sum of the quotient of 12 and –3 and the square root of 25
Show the quotient being added to
B. the difference of y and the product of 4
and
Use parentheses so that the product is evaluated first.

24. Check It Out! Example 4
Translate the word phrase into a numerical or algebraic expression: the product of 6.2 and the sum of 9.4 and 8.
Use parentheses to show that the sum of 9.4 and 8 is evaluated first.
6.2( )

25. Example 5: Retail Application
A shop offers gift-wrapping services at three price levels. The amount of money collected for wrapping gifts on a given day can be found by using the expression 2B + 4S + 7D. On Friday the shop wrapped 10 Basic packages B, 6 Super packages S, and 5 Deluxe packages D. Use the expression to find the amount of money collected for gift wrapping on Friday.

26. Example 5 Continued
2B + 4S + 7D
First substitute the value for each variable.
2(10) + 4(6) + 7(5)
Multiply.
Add from left to right. 79
Add.
The shop collected $79 for gift wrapping on Friday.

27. First substitute values for each variable.
Check It Out! Example 5
Another formula for a player's total number of bases is Hits + D + 2T + 3H. Use this expression to find Hank Aaron's total bases for 1959, when he had 223 hits, 46 doubles, 7 triples, and 39 home runs.
Hits + D + 2T + 3H = total number of bases
First substitute values for each variable.
(7) + 3(39)
Multiply.
400
Add.
Hank Aaron’s total number of bases for 1959 was 400.

28. Lesson Quiz
Simplify each expression. 2.
52 – (5 + 4)
|4 – 8|
1. 2[5 ÷ (–6 – 4)] –1 4
3. 5  8 – ÷ 22 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
6. the volume of a storage box can be found using the expression l · w(w + 2). Find the volume of the box if l = 3 feet and w = 2 feet.
24 cubic feet