Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
Review the basic rules Of arithmetic by filling in the blanks. Be as precise as possible.
I. A positive number divided by a negative number is always
2. The smallest positive factor of any positive integer is always
3. -98.7 is
(< or >) than -987.
4. A negative number times a negative number is always
5. The absolute value of (-12 -6) is
6. What is the mathematical notation for absolute value?
7. The smallest multiple of any rmmber is always
8. True or False: The remainder of 15 + 12 is 0.75.
9. True or False: 0 is a prime number.
10. The smallest prime number is:
11. TTue or False: The product of the integers from 0 to 8 inclusive is greater than the sum of the integers from 0 to
8 exclusive.
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Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
Decide whether the numbers in the left-hand column fall under any or all Of the categories at the top, and put an
"x" in the appropnate box(es). (More than one may apply for each.)
Number/Expression
Whole
Even
Odd
Negative
Positive
5,679.48
678,388
4,567.0
7 + (-2 + 4) - 9
3 - (-6 x 3) + 4 - 9
5 - (9) + (4)
I-4.31
-I-6 x 4 + 3I
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Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
Answer the questions below using the terms and concepts discussed in the chapter.
I. The quotient of 169 and 13 is
7. The product of the smallest integer in Set S and
the greatest integer in Set S is
2. The product of 6 and -2 is
8. The quotient of the value of the sum of 30 and 35
and the value of the positive differelice of 10 and
L5is
3. The absolute value of the difference between 27
and 100 is
9. (7 + 24 + 8) - 2 + (4 . 5) =
10. The product of the consecutive even integers
from 5 to 11 is
4. The product of a neutral number and 7 is
5.115 + 3 . (2 -,)I -
11. State which values each of the following
numbers are divisible by:
902:
Set S = {-7.5, -5. -1, 0,1, 2.4, 5, 7,12}
6. Th`e greatest negative integer in Set S is
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Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
9
16. -9 -(-14) + 3 x -6 =
12. If the line segment QR is divided into three equal
palts by points C and D (not shown), and C < D,
where will point C fall on the number line?
17.
How many numbers are in the set of integers
from 0 to loo, inclusive?
13. -8 + 2 x (-1) =
18. What is the smallest positive factor of 324?
14.
-26+(-11)-
-10
19. What are the distinct prime factors of 36?
15. On the number line above, what would be a good
approximation of the value of point A?
15a. If the value of point A on the line above was
multiplied by 5, draw in where the new point
(point 8) would be located.
20. What is the product of the largest odd factor
of 26, and the smallest even factor of 12?
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Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
21.
What is the difference between the sum of
the even numbers from I to 20 inclusive and
the sum of the even numbers from I to 20
26. What is ttie least common multiple of 12 and
16?
exclusive?
27. The product of the even integers from 0 to 80
inclusive is
22.
What are the factors of 12?
23.
What are the distinctprime factors ot` 12?
24.
What are the three smallest multiples of l2?
28.
What is the largest factor of the remainder
when 12 is divided by 5?
29. A pencil manufacturer produces 143,220
pencils in 55 days. Each day, they
manufacture the same number of pencils and
deliver those pencils to 7 local schools. Eacli
25.
What is the greatest common factor of I 2 and
16?
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school receives the same number of pencils.
The pencils are delivered in cases. Each case
holds a total of 124 pencils. How many cases
are delivered to each school in the month of
January?
Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
I.
Which of the following is the remainder
when 33 is divided by 6?
7.
A. 0.3
8, 0.5
C.3
D.5
2.
John works from 9 a.in. to 1 p.in. on all
days included in the set of days from
Monday to Friday, exclusive. How many
hours does John work per week?
A. 9 hours
8.12hours
C.15 hours
D. 20 hours
Which of the following is the sum of the
first 6 consecutive multiples of 25?
E. 25(1 + 2 + 3 + 4 + 5 + 6)
G. 25 . 6
Three consecutive multiples of20 have
a suni of 300. What is the least of these
numbers?
H. 6(1. 1 . 5 . 5)
E. loo
F.
8.
50 + 75 + loo + 125 + 150 + 175
F.80
G.60
H.40
3.
6+3+16+4=
A. 0.0789
8. 0.789
9.
C.5
D.6
What is the greatest common factor of72
and 90?
A.6
8.9
C.12
4.
How many distinct factors does 60 liave?
D.18
E.5
F.6
G.10
H.12
10. What is the least prime number that is
greater than 24?
E.23
F.25
5.
What is the sum of the first 4 positive
multiples of 4?
G.27
H.29
A.16
E.32
C.38
D.40
{ 1, 2, 3 ,... 75, 76, 77, 78}
6.
What is the product of the two greatest
prime numbers less than 20?
11. How maiiy numbers in the set above have 2
as a factor but do not have I 0 as a factor?
A.32
124
8.35
C.39
G. `323
D.40
E.36
F.
H. 356
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Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
JK
-17
12. If line segment JK is divided into 4 equal parts by
17. Ifg is an integer and 3g + 7 is an odd
number, which expression must represent an
even number?
points A, f, and I (not shown), where will point r
fall on the number line, if r > S > Jt?
18. Anne, Tyler, and John sold lemonade. Since
Anne provided the lemons and the cups, she
received twice the profit that Tyler and John
each received. If altogether they made $ 140
in profits, how much did Anne receive?
E. $35
F. $46
C. $70
H. $85
19. The product of two integers is -32. Which
value could be the sum of the two integers?
A. -14
14. What is the sum of the distinct factors of 24?
20. In a list of numbers that starts with 4,
every number is 6 less than three times the
number that came before it. What is the
fourth number on the list?
E.6
F.12
15. What is the greatest common factor of 108 andl44?
G.30
H.36
A.12
{1, 2, 3 ,...
123,124,125}
21. How many numbers in the set above have 5
as a factor but not I 0 as a factor?
16. The product of two positive integers is 56. Which
number could be the sum of the two integers?
A.12
8.13
E.' 12
C.25
F.18
D.37
G.23
H.27
Chapter 1 Practice
UNDATIONS I PRACTICE
ARITHMETIC FOU
22. One half the sum of two numbers is 11. If
one of the numbers is 8, what is the positive
difference between the two numbers?
E.6
F.8
n the set of all integel-s from 6 to 41,
nclusive, how many are multiples of 3 but
Lot 4?
`!
-try,
-y*..i.I
G.14
H.22
00
11
22
23. What is the greatest prime number less
33
than 53?
A.52
44
S5
8.51
66
77
88
99.ooper'sLollipopsis shipping its lollipops
C.49
D.47
24. At 8:00 p.m„ the temperature was 7 degrees.
Then the temperature fell by 4 degrees
per hour for seven hours. What was the
temperature at 3:00 a.in.?
E. 28 degrees below 0
F. 21 degrees below 0
G. 4 degrees below 0
H. 28 degrees
ITound the country. Each box of lollipops
:an hold 172 lollipops. If Looper's is
}hipping a total of I,612 lollipops and fills
ll but the last box to capacity, how many
5
llipops will go into the last box?
.9
52
.64
. 1,002[fpisan even integer less than -9.87, what
25. The temperature on Monday was 52
degrees. If the temperature rose by 4
degrees each day, what was the temperature
on Friday of that week?
A 68 degrees
8. 64 degrees
C. 56 degrees
D. 36 degrees
ls the greatest possible value ofp?
A-12
8. -10
C.-9
D. Cannot be determinedCD
_
26. In a list of numbers that starts with the
-T
number 12, every number is 11 less than
twice the number that came before it. Ih/hat
will the fifth number in the list be?
E.1
F. .15
G.19
H.27
I
I
-3 -2 -1
11
11
0
I
I
I
T
I
2
3
I
I,11111
I
4
5
6
7
8
Points A and 8 are not shown on the number
line above. IfD is the midpoint of AC. and A
is the midpoint ofDB, where on the number
line would 8 be located?
E.6
F.7
G.8
H.9
_
111111
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_
9
Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
31. Carol's salary is $31,000. DeboTah's salary
is $29,800. Carol receives a $400 annual
raise, and Deborali receives a $700 annual
raise. In how many years will Carol and
35. What is the sum of the two greatest prime
numbers less than 60?
A.112
8. 143
Deborah be eaning the same amount?
C. 200
D. 206
36. What is the product of the consecutive
positive odd integers less than 10?
I.0
F.45
G. 945
H. 362,880
32. Mark, Carlos, and Aaron shared a bag of
toys. Mark and Carlos each took twice as
many toys as Aaron took. If the number of
toys in the hag was 15, how many toys did
Aaron take?
37.
I(-5) . (-2) + (-15)I
-|17 -(-11) -33| =
A. -15
8. -10
E.3
F.5
G.6
H.9
38. The oil production facility mTis continuously
33. Jessica is making cupeakes for her school
bake sale. Each cupcake tray can hold up to
12 cupcakes. If Jessica would like to make
75 cupcakes, and fills all but the last tray to
capacity, how many cupcakes will go on the
for four 16-hour shifts and then shuts down
for maintenance. If the first shift begins at
8:00 p.in., at what time will the fourth shift
end and the maintenance process begin?
E. 2:00a.in.
F. 2,00p.in.
G.12:00a.in.
H.12:00p.in.
39. What is the product of the absolute value of
-7 and the remainder when 35 is divided by
34. The greatest common factor of 36 andy
`
4?
is 12. How many possible values for}J are
greaterthan 12 and less than 90?
A. -21
E.3
C. 5.25
F.4
D.21
G.5
H.6
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8. -5.25
Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
40. Geri and Marianne each pay S150 in utilities
for the electncity, phone, and cable bills. When
Bianca moves in, the electricity bill increases by
$30, but the other bills stay constant. If they split
all costs evenly, how mucll does each girl now
44. How many numbers from I to 167 are
divisible by 5 but not by I 5?
pay in utilities?
I. $160
F.
$110
G. $100
H. $80
41. At 5:00 p.m„ the temperature in Burlington,
Vermont was 20 degrees. Then the temperature
dropped 2 degrees per hour until 6:00 a.in.
when the sun rose the next day. What was the
temperature at 2:00 a.in.?
A. -2 degrees
8. 0 degrees
C. 2 degrees
45. On a number line, point J is located at -2, and
points J and C are 20 units apart. Point I is the
midpoint of segment LJC. If I < 0, where is I
D. 15 degrees
located?
JKL
-22
-14
-6
2
10
18
42. In the figure above, point A4-(not showli) is the
midpoint of K£. What is the length ofJIA4?
E.3
F.7
G.17
H.24
43. On a mmber line, points fJ and G are twice the
distance as points H and K, which are 5 units
apart. What is the distance between points G and
K?
A. 5 cm
8.10cm
C.15cm
D. Cannot be determined from the infomation
given
PQ
•-I
-,4-t -i
-I,
I
i
I
I
i
5'
I
'7 .
46. Point A (not stiown) is located on the line
segment above such that jig is 8 times as long
as PR. What is the location of point Jt?
E.4
F,-2
G.0
H.2
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Chapter 1 Practice
ARITHMETIC FOUNDATIONS I PRACTICE
51. Gertrude leased a storage unit for five years.
GH
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
47. Point J (not shown) is located on line
segment GfJ so that fz7 is 3 times as long as
a/. Wliat is the location of point J?
A.0
8.I
C.2
She paid a one-time fee of $850 and an
additional $28 per month for five full years.
What was her total cost for leasing the
storage unit?
A.
Sl,186
8.
$1,355
C. $2,530
D. $2,624
D.3
52. Homer operates a donut shop. Each week he
has fixed expenses of S I.425. It costs him
AB
•4
-3
-2
-1
0
1
2
3
4
5
6
7
8
48. Point C' (not shown) is located on line
segment 48 so that AC is 5 times as long as
CB. What is the location of point C,'?
E.-4
F.-2
G.2
$4 to make one box of donuts, and he sells
the box for $6. What is Homer's profit if he
makes and sells 4,200 boxes of donuts in
one week?
E. $6,975
F.
SI8,220
G. $23,775
H. $25,200
11.4
I
i
i5onB
c
i
coon
1
D
53. A restaurant has one entire shelf devoted
to cans of tomato sauce. When it is full,
it holds a total of`48 cans. Currently the
shelf is only partially filled. When the chef
removes 7 cans, the shelf is one-third full.
How many cans were on the shelf before the
chef removed any?
49. On the line above, if line segment BC is one
third the length of line segment j4C, what is
the length of line segment AJ}.J
A.18
A.16
B.18
C.21
D.23
8.21
C.25
D.30
50. Points A, 8, C, and D represent -17, -9, 2,
and 8. respectively, on a number line. How
many units is the midpoint ofAB to the
S4. The spotlight from a lighthouse completes
one revolution every 30 seconds. If the
spotlight starts moving at 6:55 p.in., at
what time will the spotlight complete 24
revolutions?
midpoint of CD?
E.2
F..8
F.
G.12
H. 7:18 p.in.
H.18
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E. 7:05p.in.
7:07p.in.
G. 7:]2 p.in.