DEV 085

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DEV 085
Unit 1 Notes Whole Numbers (brief
overview) Integers
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Whole Numbers
You should know

• Place Value
• How to Round
• 4 Basic Functions , -, x,
• Vocabulary (key words associated with the
  different operations)
• Exponents
• Order of Operations
• Problem Solving

Additional information about these topics can be
found in your notes packet. Review and practice
what is appropriate for you.
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Sidebar Multiplication Signs and Symbols
x
?
( )

• These symbols all represent multiplication. You
  multiply when
• You have a number and letter next to each other
• You have a number outside the parenthesis or
  brackets and no operation sign in between

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Another Side Bar
Perfect Squares
4 x 4 16 5 x 5 25 6 x 6 36
These are perfect squares
Square Roots
One of these is the square root
9 x 9
81
49
7 x 7
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Another Side Bar
Square Roots of Non-Perfect Squares
The square root for 22 fall somewhere between 4
and 5
25
5 x 5
22

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We can say that the square root for 22 is
approximately 5 since 22 is closer to 25 than it
is to 16
16
4 x 4
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Exponents and Exponential Notation
Exponents and Exponential Notation are used to
represent repeated multiplication
Exponent
2
5
Means 5 ? 5 25
Base
Writing in exponential notation
2 ? 2 ? 2 ? 3 ? 2 ? 3 ? 5
24 ? 32 ? 5
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Exponent Practice
Practice Expand and evaluate each.
3 ? 3 4 ? 4 ? 4 2 ? 2 ? 2 ? 2 ? 2
9 64 32
32 43 25
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Exponential Notation Practice
Practice Write each in exponential notation.
23 ? 32 2 ? 32 ? 5 23 ? 3 ? 7
3 ? 3 ? 2 ? 2 ? 2 2 ? 3 ? 3 ? 5 2 ?
2 ? 3 ? 2 ? 7
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Problem Solving
Steps for Problem Solving Step 1 Read the
problem carefully Step 2 Write down the
important information Step 3 Write down what
you need to find Step 4 Make a plan (determine
what mathematical operation you need to
use) Step 5 Do the mathematics Step 6 Check
to see if your answer is reasonable
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Finding An Average
Finding an Average Step 1 Add all items in
the given data set (group) Step 2 Divide your
sum by the total number of items in your group
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Multiple Step Problems

• Problems with Multiple Steps
• Take it one step at a time
• Be sure you are finding an answer to what you
  are asked

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Practice Story Problems
Read and solve each problem. Joe spent 145,
220, 122, 339, 267, and 81. Estimate to the
nearest hundred dollars how much Joe spent.
Joe spent 1,174
145 220 122 339 267 81
RoundedJoe spent 1,200
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Practice Story Problems
Read and solve each problem. Jack spent 14,
22, 12, 33, 26, and 82. What is the average
amount that Jack spent?
14 22 12 33 26 82
189 6 31.50
Jack spent 31.50
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Practice Story Problems
Read and solve each problem. Max went to the
baseball card show. He took 312 cards with him.
He purchased 27 cards, sold 14 cards and traded 8
cards. How many cards did he come home with?
325
312 27 14
Max came home with 325 cards
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Practice Story Problems
Read and solve each problem. Mandy counted the
quarters in her change jar. She had 187.25.
How much change would be unrolled if she rolled
as many quarters as possible? (There are 10 in
a roll of quarters).
187.25 10
18.72518 rolls of quarters
18 rolls 180 rolledleaves 7.25 unrolled
7.25 remains unrolled
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Order of Operations

• Please Excuse My Dear Aunt Sally
• The first letter in each word stands for a
  different mathematical operation
• ALL ARITHMETIC PATTERNS FOLLOW THIS PROCESS
• Remember the following phrase and youll know
  the correct order to follow

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Order of Operations
Please Excuse My Dear Aunt Sally
P Parenthesis E Exponents M Multiply D
Divide A Addition S Subtraction
Do whichever one comes first working from left
to right
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Order of Operations Practice
Practice Evaluate each problem. 2 3 x 4 ? 6
23 2 x 6 1 23 4 x 5 8 ? 2 3
(3 2)2 2 4 ? 2
4 12 32 28
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Order of Operations Practice
Practice Evaluate each problem. 3 x 52 (8
4) 2 100 5 x 4 18 - 33
77 71
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Introduction To Signed Numbers
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Introduction to Signed Numbers
Signed Numbers are numbers that are positive
and/or negative in value. -4 -3 -2 -1
0 1 2 3 4
Zero is neither positive nor negative
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Introduction to Signed Numbers
Terms associated with Signed Numbers Gain Los
s Opposites Absolute Value (written as
read as the absolute value of
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Addition With Signed Numbers
Steps for Adding Signed Numbers Like Signed
Values Step 1 Add numerical values Step 2 Put
in the appropriate sign Unlike (Different)
Signed Values Step 1 Find the difference
between the numerical values Step 2 Determine
the sign
-5 -7 -12 3 8 11 -8 4 -4 9 -7
2
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Addition With Signed Numbers Practice
Practice Find the sum for each. -3 2 -5
-8 6 -9 4 -2 -9 -2 -21 21 -5
-11 12 -8 -10 -21
-1 -13 -3 2 -11 0 -16 4 -31
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Subtraction of Signed Numbers
Steps for Subtracting Signed Numbers Step 1
Rewrite the subtraction problem as an addition
problem 1st value stays the same minus sign
becomes a plus sign 2nd value is written as its
opposite Step 2 Solve the addition problem
-5 7
-8 -9
-5 -7
-12
-8 9
1
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Subtraction of Signed Numbers
Practice Find the difference for each. -3 4
8 - -3 -6 - -3 -3 - 5
-3 -4 8 3 -6 3 -3 -5

-7
11
-3
-8
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Subtraction of Signed Numbers
Practice Find the difference for each. 7 -
12 -23 - 14 9 - -25 -14 - -22
7 -12 -23 -14 9 25 -14
22
-5
-37
34
8
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Multiplying and Dividing With Signed Numbers
Steps for Multiplying and Dividing Signed
Numbers Step 1 Multiply or divide as is done
with whole numbers Step 2 Determine the
sign If the signs are the samethe answer is
positive If the signs are differentthe answer
is negative
-2 ? -5 10 -5 ? 7 -35 -18 3 -6 -24
-12 2
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Multiplying and Dividing With Signed Numbers
Practice
Practice Find the product or quotient for
each. 3 ? -8 -5 ? -6 -21 ? -3 -12 ?
4
-24 30 36 -48
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Multiplying and Dividing With Signed Numbers
Practice
Practice Find the product or quotient for
each. 81 -9 -27 -3 -125
-10 -36 9
-9 90 12.5
-4 or 12 r. 5
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Multiplying with Exponential Values
Multiplying with Exponential Values If there
ARE parenthesis Exponent is even positive
answer (-3)2 (-3)(-3) 9 Exponent is odd
negative answer (-3)3 (-3)(-3)(-3) -27
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Multiplying with Exponential Values
Multiplying with exponential valuesIf there are
NO parenthesis Exponent only applies to the
value it touches - 32 (-1)(3)(3) -9 - 33
(-1)(3)(3)(3) -27
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Multiplying with Exponential Values Practice
Practice Find the product for
each. -42 (-5)3 (-7)2 -25
(-1)(4)(4) (-5)(-5)(-5) (-7)(-7)
(-1)(2)(2)(2)(2)(2)
-125
-16
49
-32
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Multiplying with Exponential Values Practice
Practice Find the product for
each. -33 (-6)2
(-1)(3)(3)(3) (-6)(-6)
36
-27
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Order of Operations
Please Excuse My Dear Aunt Sally
P Parenthesis E Exponents M Multiply D
Divide A Addition S Subtraction
Do whichever one comes first working from left
to right
Remember to use the rules that go with signed
numbers
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Order of Operations Practice
Practice Solve each. Remember to follow the
correct order of operations and to apply the
rules that go with signed numbers.
16 -3 (4) 8 12 -7 -3 3(-5) 7 22
3 42
4 -11 19 17
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Order of Operations Practice
Practice Solve each. Remember to follow the
correct order of operations and to apply the
rules that go with signed numbers.
(-4)(6) ? 2 3 -7 23 8 8 6
7 - 9 -2-14
undefined 10 4 -28
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Review the things that you need to review.
Study the things that you need to spend more time
on.
Ask questions about things you dont understand.
PRACTICEPRACTICEPRACTICE