Algebra 2 Fundamentals
Summer Assignment 2017
The following packet contains topics and definitions that you will be required to know in order to succeed in
Algebra 2 Fundamentals this year. You are advised to be familiar with each of the concepts and to complete the
included problems by Thursday, August 31, 2017. All of these topics were discussed in either Algebra I or
Geometry and will be used frequently throughout the year. All problems are expected to be completed.
Multiplication Tables
In order to be successful in any algebra course you must have the multiplication tables
memorized. You should know every integer multiple of the numbers one through twelve, up to
twelve. The products of any two numbers between 0 and 12 are given below. There are a few
blank tables included in this packet. Your goal is to complete an entire table in under 3
minutes without using a calculator. An explanation of how to multiply is below the table.
x
0
1
2
3
4
5
6
7
8
9
10
11
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
10
11
12
2
0
2
4
6
8
10
12
14
16
18
20
22
24
3
0
3
6
9
12
15
18
21
24
27
30
33
36
4
0
4
8
12
16
20
24
28
32
36
40
44
48
5
0
5
10
15
20
25
30
35
40
45
50
55
60
6
0
6
12
18
24
30
36
42
48
54
60
66
72
7
0
7
14
21
28
35
42
49
56
63
70
77
84
8
9
10 11 12
0
0
0
0
0
8
9
10 11 12
16 18 20 22 24
24 27 30 33 36
32 36 40 44 48
40 45 50 55 60
48 54 60 66 72
56 63 70 77 84
64 72 80 88 96
72 81 90 99 108
80 90 100 110 120
88 99 110 121 132
96 108 120 132 144
Multiplication is just repeating a given number.
When you see a problem like 3 5 , the problem is asking you
to find the total when you take 3 groups of 5 things.
Try thinking of 3 book shelves with 5 books on each shelf.
You can multiply 3 by 5 to get the total number books there are.
You can also count by 5’s three times:
five,
ten,
fifteen
1
2
3
No matter what method you use, 15 is the answer!
~YOUR GOAL~
Set a timer and try to finish every square in this table in less than 3 minutes.
DO NOT USE A CALCULATOR!
x
0
1
2
3
4
5
6
7
8
9
10
11
12
0
1
2
3
4
5
6
7
8
9
10
11
12
~YOUR GOAL~
Set a timer and try to finish every square in this table in less than 3 minutes.
DO NOT USE A CALCULATOR!
x
0
1
2
3
4
5
6
7
8
9
10
11
12
0
1
2
3
4
5
6
7
8
9
10
11
12
~YOUR GOAL~
Set a timer and try to finish every square in this table in less than 3 minutes.
DO NOT USE A CALCULATOR!
x
0
1
2
3
4
5
6
7
8
9
10
11
12
0
1
2
3
4
5
6
7
8
9
10
11
12
~YOUR GOAL~
Set a timer and try to finish every square in this table in less than 3 minutes.
DO NOT USE A CALCULATOR!
x
0
1
2
3
4
5
6
7
8
9
10
11
12
0
1
2
3
4
5
6
7
8
9
10
11
12
Division
The opposite of multiplication is division. When you divide two numbers, you are finding
how many times one number goes into another number. Numbers don’t always divide nicely,
and sometimes you will end up with a remainder. Remainders are the numbers after a decimal
point in a calculator. To succeed in algebra two you must know the following division rules.
A number is divisible by 2 if:
It is an even number. Even numbers end in: 0, 2, 4, 6, or 8.
148 is divisible by 2 because 148 is even.
A number is divisible by 3 if:
You add up all the digits of the number, and their sum is divisible by 3.
123 is divisible by 3 because 1+2+3=6 and 6 is divisible by 3.
A number is divisible by 5 if:
The numbers ends in a 0 or a 5.
955 is divisible by 5 because it ends in a 5.
A number is divisible by 6 if:
The numbers is divisible by 2 and by 3.
36 is divisible by 6 because it is even and divisible by 2 and 3+6=9 and 9 is divisible by 3.
A number is divisible by 9 if:
You add up all the digits of the number, and their sum is divisible by 9.
945 is divisible by 9 because 9+4+5=18, and 18 is divisible by 9.
A number is divisible by 10 if:
The numbers ends in a 0.
8,730 is divisible by 10 because it ends in a 0.
Identify if the given number is divisible by 2, 3, 5, 6, 9, or 10.
1] 15
2] 24
3] 112
4] 51
5] 711
6] 48
7] 50
8] 225
Decimals
Every number has only one decimal point. A decimal point is a period. Commas are not
decimal points. A comma is placed every three digits in a whole number.
14.2
 Decimal Point
If you’re given a number with no decimal, then the decimal point is after the last number.
If you are given 15 then the decimal point is to the right of the 5.
Given:
Actual:
15
15.0
 Decimal Point
Suppose you did a calculation using money. Money always has at most two decimals places.
The decimal places represent the cents in an amount of money.
Given:
Actual:
39.2
$39.20
 Cents
Write the following amounts of money in numeric form with a properly placed decimal point.
1] three dollars and twenty-five cents
2] eight dollars and forty cents
3] twenty one dollars and thirteen cents
4] sixty dollars
5] fifteen cents
6] two cents
7] one dollar and five cents
8] nineteen dollars and four cents
Fractions
Fractions will be used throughout algebra two and all math courses. It is important you
know the terminology for all the parts of a fraction, and how to work within a given fraction.
Whole Number  4
5  Numerator
6  Denominator
Simplified Fraction
A fraction whose
numerator and
denominator do not
share any factors.
Improper Fraction
A fraction whose
numerator is larger than
its denominator.
Mixed Number
A combination of a
whole number and a
fraction
Simplified
Improper
Mixed
2
5
Not Simplified
4
10
7
5
Not Improper
2
5
2
Not Mixed
3
5
3
5
To simplify a fraction you need to:
1] Divide the numerator and denominator by the same number
6 6 2 3

10 10 2 5
18 18 2 9 9 3 3


24 24 2 12 12 3 4
To convert a mixed number to and improper fraction you need to:
1] Multiply the denominator by the whole number and get an answer.
2] Take the answer and add it to the numerator to get a new answer.
3] Put the new answer over the old denominator.
4x6=24
24+5=29
4
+
x
5
6
5
6
4
4
5
6
29

6
Simplify the following fractions.
1]
4
6
2]
9
12
3]
8
10
4]
10
15
5]
8
20
6]
20
40
7]
16
24
8]
22
33
9]
4
6
10]
14
35
Convert the following mixed numbers into improper fractions
3
4
2] 5
6
8
5
6
4] 2
1
10
1
2
6] 8
3
7
8] 9
1
9
1] 2
3] 1
5] 4
7] 20
2
3
9] 10
5
6
10] 300
1
2
Rounding
thousandths
ten-thousandths
hundred-thousandths
millionths
9 .
hundredths
8
ones
7
tenths
6 ,
tens
5
thousands
4
hundreds
3 ,
ten thousands
2
hundred thousands
ten millions
1
millions
hundred millions
Rounding is trying to summarize a long number. When you summarize a number you
lose accuracy. For example if you round $5.99 to $6.00, you have summarized the number and
made it easier to work with, but we all know the difference between $5.99 and $6.00 is $0.01
or one penny. Rounding requires that you know the names of each decimal place.
1
2
3
4
5
6
123,456,789.123456
In order to round, do the following:
1] Identify what place you are to round to
2] Look at the number to the right of the place you are rounding to
A] If the number is 4 or less keep the number to its left the same
B] If the number is 5 or greater add one to the number to its left
To round 18.372 to the hundredths I would do the following:
1] I want to round the 7, so that number will either stay as 7 or go up to 8
2] To decide what to do, look at the number to the right of 7
A] 2 is less than 4, so the 7 will stay the same.
ANSWER: 18.37
Round the following numbers to the indicated decimal place.
1]Round to the hundredths: 18.281
2] Round to the hundredths: 10.729
3] Round to the tenths: 6.491
4] Round to the tens: 128
5] Round to the thousandths: 6.4552
6] Round to the hundreds: 1,960
7] Round to the hundredths: 5.123
8] Round to the tenths: 7.784
Integers
Integers are positive and negative whole numbers. Below are some examples and
counter examples of integers.
1
2
3
Integers
100 -6
-14
8
/2
1.5
Not Integers
0.7 -.3333 -4.25
The number -8 is an integer:
-8 is an integer because it is a whole number.
The number 10/5 is an integer:
10
/5 is an integer because it simplifies to 2 which is a whole number.
The number 7/3 is NOT an integer:
7
/3 is NOT an integer because it simplifies to 2.5 which is NOT a whole number.
Identify if the given number is an integer or not.
1] 18
4]
8
4
5] -1
6]
2
6
12
3
8]
9
10
3]
7]
3
2
2] -13
7
/2
9]
9
1
10]
1
1
Exponents
An exponent is an operation in math that multiplies a number by itself. The number
being multiplied is called the base. The number of times you repeat the multiplication is
determined by the exponent. Consider 23:
Base  23
 Exponent
To simplify 23 you would repeat the 2, three times and use multiplication like so:
23  2  2  2  8
ANOTHER EXAMPLE
34  3  3  3  3  81
Write out the repeats of each exponent, then multiply to solve.
1] 4 2
2] 2 4
3] 52
4] 6 2
5] 19
6] 25
7] 102
8] 43
9] 81
10] 7 2
Order of Operations
An operation is something you do with two or more numbers. There are five basic math
operations: addition, subtraction, multiplication, division, and exponents. Parentheses are not
operations, but they help tell us what order to do things. In fact, there is always an order to
simplifying math expressions. Look below for the Order of Operation and for an Acronym to
help you remember it:
Acronym
P - Please
E - Excuse
M/D – My Dear
A/S – Aunt Sally
Order of Operations
P - Parentheses
E - Exponents
M/D – Multiply & Divide
A/S – Add & Subtract
Try to remember that multiplication and division occur in the same step. To decide
which to do first just read from left to right in the problem and do any multiplication or
division as you read.
Addition and subtraction are completed in the same step as well. You will do them in
the order they appear left to right. They still occur last in the Order of Operations, but like
multiplying and dividing you will do them as you encounter them reading from left to right.
Simplify the following expression: 9  3 2  8  4
There are no parentheses or exponents so you can move on
9  3 2  8  4
As you read from left to right you can multiply 3 and 2
9684
As you read from left to right you can divide 8 by 4
962
As you read from left to right you can subtract 6 from 9
3 2
As you read from left to right you can add 3 and 2
5
Simplify the following expressions using the order of operations.
1] 10 1 4  6  2
2] 5  6  3 2  4 1
3] 8  2  10  5
4] 9 1 2  3 4
5] 10 1 4  6  2
6] 1 2  3 10  5
Operations on Integers
Negative numbers are everywhere! You have to be able to add subtract multiply, and
divide them. Luckily there are some very simple rules to do this. Let’s start with adding
Adding Negative Integers
1] If two numbers have the same sign, add the numbers and use
the sign they both had with your answer.
2] If two numbers have different signs, ignore the signs, subtract
the smaller number from the larger number, and use the sign
of the larger number with your answer.
Here are some examples:
5 4
5 4  9
Both are positive, so add the numbers and keep the positive sign
The answer is positive 9.
 3   4
 3   4  7
Both are negative, so add the numbers and keep the negative sign
The answer is negative 7.
10   4 
The signs here are different, so subtract 4 from 10.
Our numeric answer is 6, but we still need to decide on a sign.
Our answer is positive because the bigger number 10 was positive.
10  4  6
10   4  6
10   18
18 10  8
10   18  8
The signs here are different, so subtract 10 from 18.
Our numeric answer is 8, but we still need to decide on a sign.
Our answer is negative because the bigger number 18 was negative.
Simplify the following expressions using the Adding Negatives rules above.
1] 10   8
2] 4   6
3]  1   3
4] 6  7
5]  5  2
6]  9  13
Subtracting Negative Integers
1] If two numbers are subtracted, then change the subtraction to
addition and change the sign on the second number only. Now
use the addition rules.
Here are some examples:
54
5   4  1
Change subtraction to addition, and change positive four to negative.
Using the addition rules, our answer is positive one.
6   5
6   5  11
Change subtraction to addition, and change negative five to positive.
Using the addition rules, our answer is positive eleven.
10  4
10   4  14
Change subtraction to addition, and change positive four to negative.
Using the addition rules, our answer is negative fourteen.
7   2
Change subtraction to addition, and change negative two to positive.
Using the addition rules, our answer is negative five.
7  2  5
Simplify the following expressions using the Subtracting Negatives rule above.
1] 5  8
2] 7  2
3]  1   3
4]  5  6
5] 9   5
6]  6   1
Multiply and Divide Negative Integers
1] If two numbers with the same sign are multiplied or divided the
solution is always positive.
2] If two numbers with the different signs are multiplied or
divided the solution is always negative.
Here are some examples:
5 6
5  6  30
The signs are the same, so the solution is positive.
Our answer is positive 30
 3  2
 3  2  6
The signs are different, so the solution is negative
Our answer is negative 6.
18   9
18   9  2
The signs are different, so the solution is negative.
Our answer is negative 2.
 12   2
 12   2  6
The signs are the same, so the answer is positive.
Our answer is positive 6.
Simplify the following expressions using the Multiplying and Dividing Negatives rules above.
1]  3  5
2] 24   6
3] 8   4
4]  5   4
5] 2   8
6] 14  7