Prof. Israel N. Nwaguru
MATH 0306
CH. 1 & 2 - REVIEW
WORKOUT EACH PROBLEM BY SHOWING ALL THE NECESSARY STEPS.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write the number in expanded notation.
1) 48,792
Answer: 4 ten thousands + 8 thousands + 7 hundreds + 9 tens + 2 ones
Write the number in standard notation.
2) 4 ten thousands + 2 thousands + 6 hundreds + 9 tens + 5 ones
Answer: 42,695
3) 6 thousands + 8 tens
Answer: 6080
Write the number in words.
4) 64,568,009
Answer: Sixty-four million, five hundred sixty-eight
thousand, nine
Write a word name for the number in the sentence.
5) Repeating patterns in numbers like 400,040,004,000 held mystical significance for most of the members of
the village.
Answer: Four hundred billion, forty million, four thousand
Write the number in standard notation.
6) Ten million, three hundred fifty-four thousand,
two hundred three
Answer: 10,354,203
Write standard notation for the number in the sentence.
7) The distance between two stars is four trillion, three hundred seventeen billion, nine hundred eighty-eight
million miles.
Answer: 4,317,988,000,000
Answer the question.
8) What does the digit 2 mean in the number 189,247?
Answer: 2 hundreds
9) What does the digit 3 mean in the number 301,475?
Answer: 3 hundred thousands
10) What does the digit 4 mean in the number 301,475?
Answer: 4 hundreds
1
Fill in the digits for the given place values in the following whole number.
11) 52,961
ten thousands
ones
Answer: Ten thousands 5, ones 1
12) 7,839,387
hundred thousands
tens
Answer: Hundred thousands 8, tens 8
13) 4,187,382,865
billions
millions
Answer: Billions 4, millions 7
Write an addition sentence that corresponds to the situation.
14) In the metropolitan area, car dealers have 9019 foreign sports cars for sale and 4434 domestic sports cars
for sale. How many sports cars are for sale?
Answer: 9019 cars + 4434 cars = 13,453 cars
Find the perimeter.
15)
Answer: 1,469 yards
Add.
16) 9469
+ 3685
Answer: 13,154
17) 12,748 + 83 + 1529 + 41,006
Answer: 55,366
18) 19,949,386
7,208,535
144,172
+ 7,733,567
Answer: 35,035,660
2
Write a subtraction sentence that corresponds to the situation. Do not carry out the subtraction.
19) Last year the hatch-back model of a new car cost $18,027. This year's model costs $19,990. How much
more does this year's model cost?
Answer: $19,990 - $18,027 =
20) A coffee can comes packed with enough ground coffee to make 79 cups of coffee. After 37 cups have been
made, how many cups of coffee can be made with the remaining ground coffee?
Answer: 79 cups - 37 cups =
Write a related addition sentence.
21) 678 - 36 = 642
Answer: 36 + 642 = 678
22) 25 - 0 = 25
Answer: 25 + 0 = 25
23) 17 - 17 = 0
Answer: 17 + 0 = 17
Write two related subtraction sentences.
24) 95 + 0 = 95
Answer: 95 - 95 = 0 and 95 - 0 = 95
Write an addition sentence and a related subtraction sentence corresponding to the situation. You need not carry out
the subtraction.
25) An electrician needs 487 feet of 12-guage wire to do a wiring job. He has 143 feet of 12-guage wire in
stock. How much more wire does he need?
Answer: 143 +
= 487,
= 487 - 143
Solve the subtraction problem.
26) 86,958
- 14,351
Answer: 72,607
Subtract by borrowing as necessary.
6481
27) - 837
Answer: 5644
Subtract.
28) 42,704 - 8523
Answer: 34,181
Round as indicated.
29) 1435 to the nearest ten
Answer: 1440
3
30) 53,144 to the nearest hundred
Answer: 53,100
31) 2005 to the nearest hundred
Answer: 2000
Round to the nearest thousand.
32) 3,723,542
Answer: 3,724,000
33) 57,001
Answer: 57,000
Estimate the sum or difference by first rounding to the nearest ten.
34) 8487
-2633
Answer: 5860
Estimate the sum or difference by first rounding as indicated.
35) Estimate by first rounding to the nearest thousand.
3436
2456
1963
+ 5389
Answer: 12,000
Use < or > for
36) -25
to write a true sentence. Draw a number line if necessary.
-32
Answer: >
37) 0
-9
Answer: >
38) -11
0
Answer: <
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.
Solve.
39) Two Great Pyrenees mountain dogs are guarding sheep in the Pyrenees Mountains along the border of
France and Spain. Simba weighs 158 pounds and Misty weighs 125 pounds. True or false: Simba is lighter
than Misty.
Answer:
True
False
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write a multiplication sentence that corresponds to the situation.
40) Julie can bike 63 miles a day. If she can vacation for 15 days, what is the maximum distance she can cover?
Answer: 63 × 15 = 945 miles
4
What is the area of the region?
41)
78 yd
13 yd
Answer: 1014 yd2
Multiply.
42) 16,000
4000
×
Answer: 64,000,000
43) 22,316
4
×
Answer: 89,264
44) (678)(91)
Answer: 61,698
Write a division sentence that corresponds to the situation. Do not carry out the division.
45) David's company has to ship 2750 boxes of sprinklers. If a truck can hold 550 boxes, how many truckloads
does he need to ship all the boxes?
Answer: 2750 ÷ 550 =
Write a related multiplication sentence.
46) 72 ÷ 3 = 24
Answer: 24 · 3 = 72
Divide.
47) 9 219
Answer: 24 R3
48) 43 5727
Answer: 133 R 8
Solve by trial.
49) 54 ÷ n = 6
Answer: 9
5
Solve.
50) x + 300 = 680
Answer: 380
51) 784 = n · 16
Answer: 49
Solve the problem.
52) An employee was paid $58,258 during the first half of last year. During the second half she was paid $
76,872. How much more was her income during the second half?
Answer: $18,614
53) Each box of matches contains 120 matches. Boxes of matches are shipped in cartons. Each carton contains
15 boxes of matches. How many matches are in each carton?
Answer: 1800
Write exponential notation.
54) 20 · 20 · 20 · 20 · 20
Answer: 205
Evaluate.
55) 5 4
Answer: 625
Simplify.
56) 6 3 ÷ 9 - 6
Answer: 18
57) 4 · (3 + 2) 2 - 2 · (5 - 3) 2
Answer: 92
58) 320 - 3 2 · 24 ÷ (4·3 - 2·2)
Answer: 293
Find the average.
59) Scores on a math test:
72 58 72 100 58
Answer: 72
Simplify.
60) 3 × {(300 - 70 ÷ 5) - [3 · 18 - (8 - 2 · 3)]}
Answer: 702
Tell which integer corresponds to the situation.
61) A climb of 171 feet down into a subterranean cave
Answer: -171
6
62) The team gave up 7 points.
Answer: -7
Insert < or > to make the statement true.
-54
63) -98
Answer: -98 < -54
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the absolute value.
64) -99
A) 99
B) -99
C) 198
D) 0
B) -88
C) 176
D) 0
Answer: A
65) 88
A) 88
Answer: A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the following.
66) Find -(-x) when x is -281.
Answer: -281
67) Find -x when x is -86.
Answer: 86
Solve the problem.
68) -68
Answer: 68
69) 27
Answer: -27
Add.
70) -5 + (-12)
Answer: -17
71) 39 + (-7)
Answer: 32
72) 3 + (-19) + 20 + (-2) + 17 + (-13)
Answer: 6
Subtract.
73) 12 - (-18)
Answer: 30
7
74) -18 - (-16)
Answer: -2
Simplify.
75) -5 + 18 - (-20) + 16
Answer: 49
Solve the problem.
76) After one round in a card game, your score was -39 points. After the second round, your score was 30
points. How many points did you get in the second game?
Answer: 69 points
Multiply.
77) -6 · (-3) · (-19)
Answer: -342
78) (-5)(-13)(-3)0 · 9
Answer: 0
Simplify.
79) -1 10
Answer: -1
80) (-2) 4
Answer: 16
Divide, if possible.
0
81)
-11
Answer: 0
82)
-8
0
Answer: Undefined
Simplify, if possible.
-2 · 2 3 + 64 ÷4 2
83)
-2 2
Answer: - 3
84)
-5 3 + 215
6 5 - 6 - 3 -3
Answer: 30
Simplify.
85) 3[-8 + 5(-8 + 2)]
Answer: -114
8
Simplify, if possible.
86) 10 - 9 - 152
Answer: -206
Evaluate the algebraic expression.
9x + 5y
when x = 12 and y = 6
87)
3
Answer: 46
Evaluate.
88) 4x 2 + 4x + 1 for x = -3
Answer: 25
For the given expression, write two equal expressions with negative signs in different places.
16
89)
-b
Answer: -
- 16
16
and
b
b
Multiply.
90) -4(-4x - 3y + 3)
Answer: 16x + 12y - 12
91) 8(x + 9 + 8y)
Answer: 8x + 72 + 64y
Combine like terms.
92) 3x - 8y + 15 - 17x - 10 - 6y
Answer: -14x - 14y + 5
93) 8x 2 y + 6xy2 - 2x 2 y + 9xy2
Answer: 6x 2 y + 15xy2
94) -5x 7 y8 + 2x 7 y8 + 7x 7 y8 - 3x 7 y8 + 8x 7 y8
Answer: 9x 7 y8
Solve using the addition principle.
95) t - 9 = 13
Answer: 22
Solve using the division principle.
96) -8a = 56
Answer: -7
Solve using the addition or division principle.
97) 15 = b - 17
Answer: 32
9