CSN Math 104B
Applied Mathematics
Chapter 1:
Arithmetic & Prealgebra
~ Exercises ~
Jim Matovina
Math Professor
College of Southern Nevada
Ronnie Yates
Math Professor
College of Southern Nevada
 Copyright 2011, 2012 - Jim Matovina, Ronnie Yates, All Rights Reserved
Section 1.1 Exercises
1. Use Leading Digit Estimation to estimate the answers to the following problems.
a. 8.9 + 5.3 + 14.8
b. 3139 × 11
c. 4122/23
2. Use Leading Digit Estimation to estimate the answers to the following problems.
a. 19.2 + 9.3 + 48.9
b. 93 × 41
c. 2117/17
For Exercises #3 to 7, read each problem carefully and estimate the answer.
3. The distance between Joe’s house and school is 11.15 miles, and Joe goes to school 4 days a week.
Estimate the total number of miles Joe drives between home and school in one month.
4. Using the information from the previous exercise, let’s assume Joe gets 29 miles per gallon. If gas
is $3.89 per gallon and Joe only uses his car to go to and from school, approximately how much
money does he spend per month on gas?
5. Julia purchased a new Honda Accord and traveled 286 miles before refueling. If she needed 15.6
gallons of gas to fill the car’s tank, estimate her gas mileage.
6. Using the information in the previous exercise, if the cost of the gas is $3.88 per gallon, estimate
the total cost of the gas.
7. If the life span of a light bulb is 3500 hours, approximately how many weeks can you keep this
light on 24 hours a day?
8. A sign mounted on a panel in an elevator reads, “Capacity: 3300 pounds (17 people).” Do you
think the elevator can support 42 first grade children? Why?
9. For the number 5623, round to the following place values.
a. Hundreds
b. Tens
c. Ten-thousands
10. For the number 8505, round to the following place values.
a. Hundreds
b. Tens
c. Ten-thousands
11. For the number 305.697, round to the following place values.
a. Hundreds
b. Hundredths
c. Ten-thousandths
12. For the number 957.65435, round to the following place values.
a. Hundreds
b. Hundredths
c. Ten-thousandths
13. For the number 9085.445545, round to the following place values.
a. Hundreds
b. Hundredths
c. Hundred-thousandths
14. For the number 5.999999, round to the following place values.
a. Hundredths
b. Tens
c. Whole Number
15. For the number 8259.687, round to the following place values.
a. Hundreds
b. Hundredths
c. Hundred-thousands
16. Add or subtract, as indicated.
a. 5.12 + 3.8
17. Multiply, as indicated.
a. 7.14 × 1.9
b. 75.12 - 18.873
c. 51 – 8.5412
b. 35.2 × 28.491
c. 11 × 2.4592
b. 25/0.003
c. 8.5426 ÷ 2.5
22. Divide, as indicated.
b. 15.12 ÷ 2
23. Simplify the following expressions.
a. 2.5 + 3.2 × 2.4
b. 43 - 15 + 18
c. 6 × (2 + 3)3 - (9 – 4) - 8
Section 1.2 Exercises
1. Reduce the following fractions to lowest terms.
a.
21/49
b. 18/36
d.
e.
56/20
2. Multiply or divide, as indicated.
2 9
×
3 7
a.
b.
21 27
×
9 14
d.
32/40
2 12
÷
3 7
3. Add or subtract, as indicated.
4 7
+
5 5
a.
11 3
−
7 7
d.
4. Add or subtract, as indicated.
2 5
+
3 7
a.
d.
16 2
−
7 3
e.
b.
e.
b.
e.
12 3
÷
7 14
7
11
+
14 14
18 30
+
24 24
17 27
+
9 18
22 3
−
7 14
5. Convert the following fractions to decimals.
c.
22/28
f.
24/200
c.
f.
c.
f.
c.
f.
1 2 35
×
15 14
17 26
÷
3 18
32 13
−
17 17
65 24
−
12 12
12 27
−
5 15
13 26
+
4 13
a.
d.
2
8
61
4
b.
e.
5
8
c.
13
6
6. Convert the following decimals to fractions.
a.
0.8
b. 0.55
d.
3.625
e. 0.166
f.
c.
f.
22
5
18
7
0.812
0.004
7. A company uses 1/6 of its income for advertising, and 1/5 of the income for employee wages.
After the employees are paid and the advertising is complete, what fraction of the income is left?
8. Al, Betty, Chuck and Diane are to divide a cash prize for winning a contest. Since Al did more
work than the others, he gets 1/2 of the prize. Based on the work they did, Betty and Chuck each
get 1/7 of the prize. What fraction of the prize is left for Diane?
9. While cooking pastries, a cook uses 2/3 cup of sugar for cookies, 1 1/2 cups of sugar for a cake,
and 1/8 cup of sugar for a special topping. How much sugar was used all together?
10. Joe’s truck can hold 23 1/2 gallons of gas. If he can go 10 1/2 miles per gallon, how far can he go
on a full tank?
11. Maria knows it will take 1 1/3 gallons of paint to paint a bedroom in her house. How many
gallons will she need to paint 5 bedrooms with the exact same measurements?
12. A driver completed a 400-mile race in 3 1/3 hours. What was her average speed?
Section 1.3 Exercises
For Exercises #1-8, simplify each expression by combining like terms.
1.
4y + 8y
2.
24x – x
3.
12a + 3b – 9a + 2b – 7
4.
14z + 6y
5.
11x – 12
6.
2a + 3 – 4a + b – 14
7.
(4a + 4p) + (2a - 9p)
8.
(15m + 4n) + (3m + 7n) – 8n + 11m
9.
Is x = 3 a solution to 3x – 9? Why or why not?
10.
Is y = 3 a solution to 3x = 9? Why or why not?
11.
Is a = 3 a solution to 3a – 6 = -3? Why or why not?
12.
Is c = 4 a solution to 3c – 6 = 9? Why or why not?
For Exercises #13-18, indicate the value that needs to be added to both sides of the equation in order
to isolate the variable, and then determine the solution to the equation.
13.
x – 8 = 12
14.
y – 14 = 39
15.
x + 13 = 12
16.
x + 11 = -9
17.
a + 19 = 12
18.
m + (–6) = 18
For Exercises #19-24, indicate the fraction that needs to be multiplied by both sides of the equation by
in order to isolate the variable, then determine the solution to the equation.
19.
5x = 45
20.
-3y = 18
21.
4c
=8
11
22.
32 = 3x
23.
8y = 0
24.
−2c 4
=
5
35
For Exercises #25-34, solve the equation.
25.
2x – 8 = 28
26.
2y + 8 = 20
27.
3m + 2 = -13
28.
-7x – 8 = 34
29.
9 + 13x = 35
30.
8 + 7x = 20
31.
32.
33.
12 = 8x - 28
2c
− 6 = 14
3
7x
+ 14 = 3
3
12 =
34.
2c
− 28
3
Section 1.4 Exercises
1. Two friends want to share the last cookie. Describe how it may be divided using the DividerChooser method.
2. Three brothers are left a ukulele by their Uncle Liho. They will use the Method of Sealed Bids and
each person puts forth a bid as follows. What will be the final distribution?
Item
Amos
Barry
Chuck
Ukulele $60
$90
$120
3. Four siblings will use the Method of Sealed Bids to determine who gets the family dog, with the
bids as indicated below. What will the final distribution be?
Item
Tom
Dick
Mary
Alice
Fido
$124
$108
$96
$80
4. The semester has ended and three roommates need to choose who gets to keep the television.
They will use the Method of Sealed Bids and each person puts forth a bid as follows. What will be
the final distribution?
Item
Mickey
Willie
Ted
TV
$330
$414
$480
5. A quartet has broken up. The four members will use the Method of Sealed Bids to divide their
private plane, with the bids as indicated below. What will the final distribution be?
Item
Soprano
Alto
Tenor
Bass
Plane
$76,000
$80,000
$68,000
$72,000
Section 1.5 Exercises
1. A student started out poorly on his first mathematics test. However, he tripled his score on each
of the next two tests. The third test grade was 72. What was the student’s average test grade?
2. A large drum filled with water is to be drained using a small opening at the top. One 2-inch
diameter hose or four 1-inch hoses can be used to siphon out the water. Would it be faster to use
the 2-inch hose or the four -inch hoses? Why?
3. The cost of a car increases by 30% and then decreases by 25%. Is the resulting price of the car
greater than, less than, or equal to the original price of the car? Why?
4. A new high school graduate receives two job offers: Company A offers a starting salary of $25,000
a year with a $100 raise every month, while Company B offers $25,000 a year with a $1300 raise
every year. Which offer will provide the most income?
5. Fill in the three blanks using some combination of the symbols +, -, ×, and ÷ to make a true
statement of equality.
6___ 6 ___ (6 ___ 6) = 1
6. While visiting a friend's home, I saw kittens and children playing in the backyard. Counting
heads, I got 17. Counting feet, I got 54. How many kittens and how many children were there?
7. Determine the pattern and then generate the next two iterations for the following.
37 × 3 = 111
37 × 6 = 222
37 × 9 = 333
8. Place the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 18 in the squares below so that the sum of the
numbers in every column, row, and diagonals is equal to 30.
9. Peter, Paul, and Mary are three sports professionals. One is a tennis player, one is a golfer, and
one is a skier. They live in three adjacent houses on City View Drive. From the information
below determine who the professional skier is.
o Mary does not play tennis.
o Peter does not play golf.
o The golfer and the skier live beside each other.
o Three years ago, Paul broke his leg skiing and has not tried it since.
o Mary lives in the last house.
o The golfer and the tennis player share a common backyard swimming pool.
10. The time in New York City is one hour ahead of the time in St. Louis, and three hours ahead of the
time in Las Vegas. If a flight left NYC at 9 AM, stopped in St. Louis for 50 minutes, and then
arrived in Las Vegas at 1:35 PM, how long was the plane actually flying?
11. If the following pattern is continued, how many dots will be in the hundredth figure?
12. A man who has a garden 5 meters square (5 m by 5 m) wishes to know how many posts will be
required to enclose his land. If the posts are placed exactly 1 m apart, how many are needed?
Disregard the thickness of the posts. How many will he need if his garden is 8 meters square? 12
meters square?
13. Determine the pattern and then generate the next two iterations for the following.
92 = 81
992 = 9801
9992 = 998,001
99992 = 99,980,001
14. Cindy was given her allowance on Monday. On Tuesday she spent $2.50 on candy. On
Wednesday, Cindy found $1.50 on the ground. If Cindy now has $4, how much was her
allowance?
15. John, Paul, and George uncovered a treasure chest containing some diamonds. They buried half
of the diamonds and divided the remaining diamonds evenly among themselves. John received
15 diamonds. How many diamonds were in the treasure chest when they found it?
16. Joe walked from his home to Susan’s in 35 minutes. Then, together, it took Joe and Susan 20
minutes to walk from Susan’s house to school. If they arrived at school at 7:25 AM, what time did
Joe leave his home?
17. Gym lockers are to be numbered from 1 to 100 using metal numbers to be glued onto each locker.
How many 1's are needed?
18. At the beginning of the bake sale, Mary set aside 4 pies for herself. Karen then bought half of the
remaining pies, and 5 more pies were sold during the sale. When the sale was over, there were 6
pies remaining. How many pies were there before the bake sale started?
19. Calculators were purchased at $65 per dozen, and sold at $20 for three calculators. Find the profit
for selling eight dozen calculators.
20. A backyard fair charged $1.00 admission for adults and $0.50 for children. The fair made $29 and
sold 38 tickets. How many adult tickets were sold?
21. Mike wants to cut a log into 16 pieces. How many cuts are necessary?
22. A person has 20 coins consisting of dimes and nickels. If the person has a total of $1.45, find the
number of nickels.
23. Use your calculator to determine the squares of 75, 175, 275, 375 and 475. Use this pattern to
predict the square of 575 and 675.
24. 111,111,111/12,345,679 = 9
222,222,222/12,345,679 = 18
333,333,333/12,345,679 = 27
444,444,444/12,345,679 = 36
What is 888,888,888/12,345,679? (Use the pattern, not your calculator!)
25. 112 = 121
1112 = 12,321
1,1112 = 1,234,321
11,1112 = 123,454,321
What is 111,1112? (Use the pattern, not your calculator!)