College Math Topics
Summer Packet
Monmouth Regional High School
This summer review assignment is for students enrolled in College
Math Topics to refresh your basic math skills and prepare for a
successful year! The purpose of the course is to elevate your math
skills so you are placed in a college level course upon entering college.
Basic math sense is essential to successfully complete the higher level
lessons of the course.
π The packet is to be completed by the first day of school.
π It will be collected and graded based upon completion and effort.
π To receive full credit on the summer work, every problem must be
attempted even if the final answer was not obtained.
π Because these are not new concepts, topics in this packet will be reviewed at
a rapid pace during the beginning of the school year.
π All of the concepts in the packet are math skills that you should had
learned in your previous math classes.
π A formal assessment will be given based on information reviewed
in this packet during the first week of school in September.
π You will be required to take this assessment even if you are absent for the
in-class review sessions.
π When necessary, use the formulas provided in this packet and online sites to
help refresh your memory!
π You MUST show all work for each problem in order to receive
credit!
π Show all work and answers directly in the packet.
OPERATIONS WITH POSITIVE AND NEGATIVE INTEGERS
(No Calculator)
Addition and Subtraction of Integers
A. Adding Positive and Negative Numbers
If the signs are the same, add them and keep the sign.
 To add two positive numbers, add and keep the positive sign
Example: (+6) + (+7) = +13

To add two negative numbers, add and keep the negative sign
Example: (-13) + (-24) = -37
If the signs are different, find the difference between the two numbers (subtract) and give
the answer the sign of the number with the greater absolute value.
Example #1:
(+17) + (-6) =
(+17) – (+6) = 11
|+17| > |-6| so use the sign from 17 (positive)
(+17) + (-6) = +11
Example #2:
(-32) + (+18) =
(+32) – (+18) = 14
|-32| > |+18| so use the sign from 32 (negative)
(-32) + (+18) = -14
B. Rules for Subtracting Positive and Negative Numbers
To subtract signed numbers (either positive or negative), change the subtraction sign to
an addition sign and change the sign of the number that follows. Then use the addition
rules above.
Example #1:
Example #2:
Example #3:
Example #4:
(+8) - (+5) = (+8) + (-5) = +3
(+7) - (-4) = (+7) + (+4) = +11
(-12) - (+6) = (-12) + (-6) = -18
(-23) - (-16) = (-23) + (+16) = -7
C. Rules for Multiplying and Dividing Positive and Negative Numbers
With both multiplication and division, when the signs are the same, the answer will be
positive
Example #1: (+5) × (+7) = +35
Example #2: (-5) × (-7) = +35
Example #3: (+10) ÷ (+2) = +5
Example #4: (-10) ÷ (-2) = +5
When the signs are different in a multiplication or division problem, the answer will be
negative
Example #1: (+8) × (-7) = -56
Example #2: (-12) × (+4) = -48
Example #3: (+9) ÷ (-3) = -3
Example #4: (-14) ÷ (+2) = -7
When you multiply several factors, if the number of negative factors is odd, then the product is
negative. If the number of negative factors is even, then the product is positive.
Example #1:
(-6)(-2)(3)(-5) = negative because there are an odd number (three)
negative factors.
The product is -180.
Example #2:
(7)(-4)(-2)(3) = positive because there are an even number (two) of
negative factors.
The product is 168.
PRACTICE SHEET
A. Solve the following problems without a calculator.
1. -2 + (+3) =
11. -3(-4) =
21. 45 - (-27) =
2. -5 + (+4) =
12. 24 ÷ (-6) =
22. 19(-4) =
3. 5 - (-3) =
13. 5(-18) =
23. -42 ÷ (-6) =
4. -7 - (-3) =
14. -8 ÷ (-4) =
24. -21 + -19 =
5. -14 - 6 =
15. 17(-4) =
25. 32 ÷ (-4) =
6. 6 + (-8) =
16. 81 ÷ (-9) =
26. 14 - (-7) + (-2) =
7. 12 + (+7) =
17. -21 ÷ (-7) =
27. -8 • -4 ÷ -2 =
8. -8 + (-1) =
18. -7(9) =
28. -24 ÷ 4 + -17 =
9. -9 - (+6) =
19. 8(7) =
29. 7 - (-3) + (-2) - 4 =
10. 11 + (-2) =
20. 56 ÷ (-14) =
30. 12 + (-7) - (-28) =
D. Order of Operations
When several mathematical operations are in a problem, you must follow a specific order
for solving the problem. Perform the operations in the first step before moving on to the
operations in the next step.
Step 1 – Do anything that is inside grouping symbols:
 Parentheses;
 Brackets;
 Absolute Value bars;
 Radicals;
 Numerator and Denominator;
 etc..
Step 2 - Solve anything that contains an exponent or a radical.
Step 3 – Solve any multiplication or division, moving from left to right.
Step 4 – Solve any addition or subtraction, moving from left to right.
Example #1: -2(12 – 8) + -33 + 4 • -6
-2(4) + -33 + 4 • -6
-2(4) + -27 + 4 • -6
-8 + -27 + -24
-35 + -24
-59
Example #2:
-3 +
-3 +
-3 +
-3 +
-11
4|2 – 6| ÷ (-2)
4(4) ÷ (-2)
(16) ÷ (-2)
(-8)
If the operations to be performed are in fractional form, solve the numerator first, then the
denominator, then reduce.
Example: 7(-4) - (-2)
8 - (-5)
=
(-28) - (-2)
13
=
-26
13
=
-2
B. Use order of operations to solve the following problems.
1. 18 - (-12 - 3) =
7. -19 + (7 + 4)3 =
2. 18 + (-7) • (32 – 6) =
8. -19 - (-3) + -2(8 + -4) =
3. 20 + -4(32 - 6) =
9. -3 + 2(-6 ÷ 3)2
4. 3 • (-4) + (52 + -4 • 2) - (-9.82) =
10. 23 + (-16) ÷ 42 • 5 - (-3) =
5. -6(12 - 15) + 23 =
11. 4(-6) + 8 - (-2) =
15 – 7 + 2
6. -50 ÷ (-10) + (5 - 3)4 =
12. 1.4(4.7 – 4.9) - 12.8 ÷ (-0.2) =
-4.5 • (-0.53) + (-1)
E. Solve the following word problems using positive and negative numbers. Be sure to
write down all your calculations.
1. Steve has overdrawn his checking account by $27. His bank charged him $15 for
an overdraft fee. Then he quickly deposited $100. What is his current balance?
2. Joe played golf with Sam on a special par 3 course.. They played nine holes. The
expected number of strokes on each hole was 3. A birdie is 1 below par. An eagle
is 2 below par. A bogie is one above par. A double bogie is 2 above par. On
nine holes Frank made par on 1 hole, got 2 birdies, one eagle, four bogies, and
one double bogie. How many points above or below par was Franks score?
3. Find the difference in height between the top of a hill 973 feet high and a crack
caused by an earthquake 79 feet below sea level.
4. In Detroit the high temperatures in degrees Fahrenheit for five days in January
were -12°, -8°, -3°, 6°, -15°. What was the average temperature for these five
days?
5. Hightop Roofing was $3765 in the “red” (owed creditors this amount) at the end
of June. At the end of December they were $8765 in the “red.” Did they make
or lose money between June and December? How much?
6. To establish the location of a hole relative to a fixed zero point, a machinist must
make the following calculation:
y = 5 - (3.750 - 0.500) - 2.375
Find y.
Converting between decimals and fractions
To change a decimal to a fraction: use the place value of the last digit.
÷5
For example
85 = 17
0.85 = 100
20
÷5
hundredths
To change a fraction to a decimal: divide the top by the bottom
For example
4 = 4  5 = 0.8
5
Converting from percentages to decimals
To write a % as a decimal: Drop the percent sign and move the decimal point two places
to the LEFT.
Example #1: 64%
64
= 0.64
Example #2: 1.2%
1.2
= 0.012
Converting from percentages to fractions
To write a % as a fraction: Divide the percent value by 100 (and reduce)
Example #1:
64 = 16
64% = 100
25
Example #2:
1.2% = 100 = 1000 =
1.2
12
3
250
Converting from decimals to percentages
To write a decimal as a %: Move the decimal point two places to the right and add a
percent sign.
Example #1:
0.125
12.5
12.5%
Example #2:
0.3
30.0
30%
Converting from fractions to percentages
To write a fraction as a %: Either convert the fraction to decimal and convert as above,
𝑛
or set up a proportion of the fraction equal to 100 and solve for n.
Example #1:
2 = 2  5 = 0.4 = 40% or
5
Example #2:
2 = 𝑛
5 100
200 = 5n
n = 40
40%
Try these
1 Write these decimals as fractions:
0.3 = ………….
0.5 = ………….
0.6 = ………….
0.02 = ………….
0.05 = ………….
0.25 = ………….
0.36 = ………….
0.125 = ………….
2 Write these fractions as decimals:
7
10 = ……………….
1 = ……………….
5
2 = ……………….
5
3
4 = …………………
7
8 = ……………….
2 = ……………….
3
9
20 =……………….
7
25 = …………………
3 Write these percentages as decimals:
3% = ………….
30% = ………….
25% = ………….
80% = ………….
8% = ………….
12% = ………….
67% = ………….
17.5% = ………….
4 Write these percentages as fractions:
20% = ………….
75% = ………….
5% = ………….
30% = ………….
40% = ………….
15% = ………….
24% = ………….
35% = ………….
5 Write these decimals as percentages:
0.25 = ………….
0.5 = ………….
0.7 = ………….
0.07 = ………….
0.45 = ………….
0.09 = ………….
0.4 = ………….
0.375 = ………….
6 Write these fractions as percentages:
1
10 = ………….
1 = ………….
5
9
10 = ………….
3
4 = ………….
4 = ………….
5
17 = ………….
20
1 = ………….
3
2 = ………….
3