1. A#17 / 1-5 Homework Worksheet
Homework Corrections
A#17 / 1-5 Homework Worksheet
1. a) 11
b) 20
c) -10 yd
3. a) real number, ;
rational number,
b) real number, ;
rational number, ;
integer,
3. c) real number, ;
irrational number
4. a) b) c)
5. a) always true
b) sometimes true
c) always true

2. Warm Up Simplify. 1. 42 2. -23 3. |5 – 16| 4. |3 – 7|
3. |5 – 16| |3 – 7|
Simplify each fraction.

3. Lesson Objective: I will be able to …
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Lesson Objective: I will be able to …
Use the order of operations to simplify
expressions
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

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

5. Helpful Hint The first letter of these words can help you
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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 and Divide (from left to right)
Add and Subtract (from left to right
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.

6. Example 1: Simplifying Numerical Expressions
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Simplify each expression.
A. 15 – 2 · 3 + 1
There are no parentheses or exponents.
15 – 2 · 3 + 1
Multiply.
= 15 – 6 + 1
Subtract and add from left to right.
= 10
B. 12 – ÷ 2
There are no parentheses.
12 – ÷ 2
Evaluate exponents.
= 12 – ÷ 2
Divide.
= 12 – 9 + 5
Subtract and add from left to right.
= 8

7. Simplify the expression.
Your Turn 1
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Simplify the expression.
5.4 –
There are no parentheses.
= 5.4 –
Simplify exponents
= 5.4 –
Subtract and add from left to right.
= –
= 2.6

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

9. Evaluate the expression for the given value of x.
Your Turn 2
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Evaluate the expression for the given value of x.
(x · 22) ÷ (2 + 6) for x = 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.

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

11. Your Turn 3 Simplify: |4 – 7|2 ÷ (–3) = |–3|2 ÷ –3 = 32 ÷ –3 = 9 ÷ –3
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Simplify:
|4 – 7|2 ÷ (–3)
The absolute-value symbols act as grouping symbols. Subtract within the absolute-value symbols.
= |–3|2 ÷ –3
= 32 ÷ –3
Write the absolute value of –3.
= 9 ÷ –3
Square 3.
= –3

12. Example 4: Translating from Words to Math
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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.

13. Translate the word phrase into a numerical or algebraic expression:
Your Turn 4
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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( )

14. Cornell Notes Fill in the Essential Question:
“How do I simplify expressions using the order
of operations?”
Write two or three main ideas from this lesson
in the Notes section.
Write a Question for each main idea.
(The answer to the question should be the
main idea.)
Summarize the answers to your questions in
the Summary section.
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15. Classwork
Ladder Activity: Order of Operations

16. Homework Assignment #18 Finish 1-6 Homework Worksheet
Chapter 1 Quiz Friday!