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Math 090 Exam 1 Review- Chapter 1, 2.2 & 2.3
Section 1.1
Whole Numbers: Writing, Rounding, and Inequalities
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
Natural numbers (counting numbers): 1, 2, 3, 4, 5, and so on
Whole numbers: 0, 1, 2, 3, 4, 5, 6, and so on.
Place value notation: numbers larger than 9 are written in place value notation by writing the
digits in positions having standard place value
Less than symbol <
Greater than symbol >
Round – to give a number an approximate value by rounding to an indicated place.
Name the place value of the indicated digit in the number 15,287,654
1. the 1
2. the 6
Write the word name for:
3. 23, 001
4. 5, 408, 325
Write the place value notation for:
5.
Thirty-five thousand, four hundred six
6. Twelve million, seventy-six thousand, five
Compare the numbers using < or >
7. 6507____6570
8. 1410____1140
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Round to the indicated place value:
9.
Round 985,237 to the ten thousand’s place
10. Round 3, 999 to the hundred’s place
Section 1.2 Adding and Subtracting Whole Numbers
Addends - the numbers that are added
Sum - the answer to an addition exercise
Difference - the answer in a subtraction exercise
Term - numbers or variables that are added.
Ex. In the expression 3 + 4, 3 and 4 are both terms.
Properties of Addition:
Commutative Property of Addition: a + b = b + a
Associative Property of Addition: (a + b) + c = a + (b + c)
** Note that the commutative and associative properties do not apply to subtraction.
Find the sum of:
11.
65,
4,432 and
908, 324
12.
35, 532, 6,859 and 3,001
Subtract (Find the difference of):
13.
36,123 and 5,987
14.
598,225 and 16, 549
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Section 2.2
Perimeter
Polygon – any closed figure whose sides are line segments
Perimeter – the distance around the outside of a polygon.
Find the perimeter: (Include proper unit values.)
15.
Perimeter of a rectangle = 2(length) + 2(width)
16 cm
9 cm
16.
14 in.
12 in.
Section 1.3 Multiplying and Dividing Whole Numbers
Factors – the numbers being multiplied in a multiplication exercise.
Product – the answer to a multiplication exercise.
Ex. In the equation 4 5 = 20 4 and 5 are the factors, and 20 is the product.
Properties of Multiplication:
Commutative Property of Multiplication: a  b  b  a
Associative Property of Multiplication:
a  (b  c)  (a  b)  c
Distributive Property: a  (b  c)  a  b  a  c
Multiplication Property of Zero: a  0  0  a  0
Multiplication Property of One: a 1  1 a  a
**Note that the commutative and associate properties do not apply to division.
Dividend – the number being divided
Divisor - the number we are dividing by
Quotient – the answer to a division exercise
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Remember:
0
0
any number
any number
is undefined
0
Multiply (or Find the product of):
17.
435
169 =
18.
925
728 =
Distribute:
19.
5  (34 + 26) =
20.
13  (16 + 20) =
Divide (or Find the quotient of):
21. 5,688  18 =
22.
55, 269
=
13
23. What is the remainder of 200 divided by 10?
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Match the letter of the property that was used with the corresponding equation.
24.
4
1 = 4 __________________________
A. Associative
25. 2 + 9 = 9 + 2______________________ ___
B. Commutative
26. 3(2 + 1) = 6 + 3_______________________
C. Distributive
27. 3   6  7    3  6   7 ___________________
D. Multiplicative Identity
Section 2.3 Area
Area – a measure of surface (measured in square units)
Base – the side of a geometric figure that is parallel to the horizon
Altitude or Height – the perpendicular distance from the base to the highest point of the figure
Formulas:
Area of a rectangle = length  width
Area of a triangle =
base  height
2
A  l w
A
bh
2
Find the area of the following figures: (Include proper unit values.)
28.
Area of a rectangle = length  width
15 ft
6 ft
29. Area of a triangle =
6 cm
10 cm
base  height
2
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Section 1.4 Whole Number exponents and Powers of Ten
Base – a number used as a repeated factor
Exponent – indicates the number of times the base is used as factor
Ex. With 53 5 is the base and 3 is the exponent
Properties of Exponents:
1. If 1 is used as an exponent, the value is equal to the base. x1  x
2. If 0 is used as an exponent, the value is 1 (unless the base is also 0). x 0  1
Evaluate:
30.
53
31.
500
Multiply as indicated:
32.
34  105
33.
356  107
Divide as indicated:
34. 3, 256,000  103
35. 55,879,000,000  10 4
Section 1.5 Operations with Exponents
Rules of Exponents:
1. To multiply powers with the same base, add the exponents and keep the common base.
Ex. x a  x b  x a b
2. To divide powers with the same base, subtract the exponents and keep the common base.
Ex.
xa
 x a b
xb
3. To raise a power to a power, multiply the exponents.
Ex.
x 
a b
 x ab
4. To raise a product to a power, raise each factor to the power.
Ex.
 x  y
a
 xa  y a
5. As covered in section 1.4, any number to the power of 0 = 1.
0
Ex. x  1
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Use the rules of exponents to simplify, but DO NOT EVALUATE!
36. 154 1510 157
37.
615
69
38.
5 7 
39.
40.
4 5 3
85  87
83  87
63  62 
4
6  65
41.
40  45
42.
58  54  36
53  32
Section 1.6 Order of Operations and Average
To simplify an expression with more than one operation follow these steps:
Step 1: Parentheses
Step 2 : Exponents
Step 3: Multiply and Divide – do only multiplication and division as they appear from
left to right
Step 4: Add and Subtract - do addition and subtraction as they appear from left to right.
Story Problem Review:
1.
Read the problem
2. Determine which math function to use
3. Set up the equation
4. Solve and label your answer
5. Reread the problem to make sure that you have answered the question.
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Evaluate:
43. 34  3 10  2  6
44.  4  6  2    8  3  16
2

45. 13  13 33  6 13
0

Find the average of:
46. 23, 15, 22
47. 56, 27, 9, 28
Story Problems:
48. Christie took four tests in her math class. She scored a 95 on the first and the third test, a 79 on
the second test, and an 87 on the fourth test. What was her average score?
49. Ben went out jogging. It took him 7 minutes to run 2 laps. How long would it take him to run
22 laps?
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Answers to 090 Exam 1 Review
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35.
ten million’s place
hundred’s place
Twenty-three thousand, one
Five million, four hundred eight
thousand, three hundred twenty-five
35,406
12,076,005
<
>
990,000
4,000
912,821
10,427
30,136
581,676
50 centimeters
52 inches
73,515
673,400
300
468
316
4251 R 6
0
D
B
C
A
90 square feet
30 square centimeters
125
1
3,400,000
3,560,000,000
3,256
5,587,900
36. 1521
37. 66
12 15
38. 5 7
2
39. 8
5
40. 6
41. 45
42. 59 34
43. 43
44. 64
45. 22
46. 20
47. 30
48. Christie’s average score was an 89.
49. It would take Ben 77 minutes to run 22
laps.