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2-1 Integers and the Number Line
Whole numbers: {0, 1, 2, 3…}
Integers: {…,-3, -2, -1, 0, 1, 2, 3…}
Ex. 1: Name the coordinate of each point. (Provide number lines)
A
D
C
F
B
E
<--+---●---+---●---+---●---+---●---+---+---+---●---+---+---+---●->
-7
-6
-5 -4
-3 -2
-1
0
1
2
3
4
5
6
7
8
A -6
B 4
C -2
D -4
Name the set of numbers graphed.
Ex. 2: <--+---●---+---+---+---●---+---●---+---+---●---+->
-5
-4
-3
-2
-1
0
1
2
3
4
5
-8
-7
-6
-5
-4
-3
-2
-1
0
F 0
{-4, 0 , 2 , 5}
6
Ex. 3: ◄--●---+---●---+---●---+---●---+---●---+---+---+->
-10 -9
E 8
{…,-6, -4, -2}
1
Graph each set of numbers on a number line.
Ex. 4: {1, 3, 5, …}
Ex. 5: {integers between –2 and 4}
To simplify on a number line:
Remind students to get this from the website!
1st
Start at zero
2nd
Look at the first number and go in the direction of the sign that number of
spaces. Put a line where you stop and use an arrow to show the direction
you moved.
3rd
From that stopping point, move the direction of the sign of the next
number that number of times.
th
4
Keep repeating until all the numbers are done.
5th
When you have finished, circle the ending number and write the answer.
Using a number line, simplify.
Ex. 6: 6 + (-1)
5
Ex. 7: (-2) + (-5)
-7
Ex. 8: 6 + (-9)
-3
Ex. 9: 4 + 2
6
Ex. 10: (-5) + 8
3
Activity: Overhead problems
Using a number line simplify. (Provide number lines)
1)
3 + (-7)
2)
(-1) + (-8)
3)
6 + (-1)
4)
2 + (-10)
5)
4+5
Homework:
2-1
p. 75 #16-38 Even
(Give number line worksheet)
Algebra One – CP 2 Chapter 2 Notes
2-3
Adding and Subtracting Integers (Power Point)
The absolute value of a number is its distance from zero on the number line. Since distance is
always positive, the absolute value of a number is always positive.
| -5 | = 5
|5|=5
|½|= ½
| -½ | = ½
Rules for adding signed numbers
 When adding numbers with the same signs, add the absolute value of each number
and take the common sign.
 When adding numbers with different signs, subtract the smaller absolute value from
the larger absolute value and take the sign of the larger absolute value.
Additive Identity Property (Add. ID. Prop.)
Adding zero to any number will not change the value of that number.
a+0=a
* The additive identity is zero.
Additive Inverse Property (Add Inv. Prop.)
Adding a number to its inverse will result in zero.
a + (–a) = 0
* If two numbers are opposites, they are additive inverses of each other.
Simplify. State thought process (Add/Subtr/Add ID Prop./Add Inv. Prop.)
1)
(-4) + (-10)
2)
6 + (-7)
3)
17 + 0
-14 add
-1 subtr
17 add. ID Prop.
4)
11x + (-2x)
9x subtr
5)
(-3) + 3
0 add inv. Prop
6)
(-15x) + 4x
-11x subtr
Subtraction Rule:
To subtract, change to adding the opposite and then follow the rules for adding signed
numbers.
Simplify. Show you are using the subtr. rule and state thought process (Add/Subtr/Add ID
Prop./Add Inv. Prop.)
7)
3–5
8)
(-4) – 12
9)
(-6) – (-14)
-2 subtr
16 add
8 subtr
10)
10x – (-7x)
17x add
11)
(-9) – (-9)
0 add inv. Prop
12)
(-3x) – (-10x)
7x subtr
Evaluate if w = 14, x = -8, and y = -10. State thought process (Add/Subtr.)
13)
|x|
14)
|3–w|
15)
|w|+|y|
8
11
24
Activity: Integer Line Up
Homework:
p. 90
#26 – 54 Even
Algebra One – CP 2 Chapter 2 Notes
2-4 Rational Numbers
A Rational Number is a number that can be expressed in the form
a
b
, where a and b are integers
and b  0.
An Irrational Number is a number that cannot be expressed in the form a/b, where a and b are
integers and b  0. (Decimals that do not repeat or do not terminate.)
The set of rational numbers and irrational numbers together form the set of Real Numbers.
Recall from 2-1:
Rational
Integers: {…, -3, -2, -1, 0, 1, 2, 3,…}
Whole Numbers:
{0, 1, 2, 3,…}
Natural Numbers:
{1, 2, 3,…}
Irrational
Integers
Whole
Natural
State the set(s) each number belongs to: Whole (W), Rational (Q), Integer (Z),
Natural (N), or Irrational (I).
1)
¼
2)
3)
-8
4)
0
18
Q
I
Q, Z
Q, Z, W
5)
6)
16
Q, Z, W, N
8
3
7)
Q
19.5
Q
8)
13
Q, Z, W, N
Comparing numbers on a number line: Numbers on the left are less than numbers on the
right. Numbers on the right are greater than numbers on the left.
Comparision Property:
sentences is true.
a<b
For any two numbers a and b, exactly one of the following
a=b
a>b
Comparision Property for Rational Numbers:
b > 0 and d >0:
1)
if a/b < c/d, then ad < bc, and
For any rational numbers a/b and c/d, where
2)
if ad < bc, then a/b < c/d
Replace each ? with <, >, = to make the statement true. (You must show work!)
9)
21/30 ? 7/10
10)
6/11 ? 8/9
11)
-7/5 ? -11/6
210 = 210
63 < 88
-42 > -55
Write the numbers in order from least to greatest.
12)
7/18, 1/6, 1/3
1/6, 1/3, 7/18
Find a number in between the given numbers.
13)
1/9 and 3/5
6/45(2/15) – 26/45
Homework:
On Green Worksheet
Algebra One – CP 2 Chapter 2 Notes
2-5 Adding and Subtracting Rational Numbers
Recall:
* Rules for adding signed numbers
-When adding numbers with the same signs, add the absolute value of each number and
take the common sign.
-When adding numbers with different signs, subtract the smaller absolute value from the
larger absolute value and take the sign of the larger absolute value.
* To subtract, change to adding the opposite and follow the rules for adding signed numbers.
* To add or subtract fractions, you must have a common denominator.
* To add or subtract decimals, line up the decimals
Simplify. State your thought process (Add/Subtr.) and show that you are using the subtraction
rule. Answers should be reduced fractions or mixed numbers. If the problem had decimals, so
can your answer.
11 5
1  5

 
1)
-8.007 + (-5.755)
2)
3)
16 8
6  6
-13.762
-2/3
1 5/16
4)
6.32 – (-3.4)
9.72
5)
 1  6
  
 2  7
5/14
Evaluate each expression. State your thought process (Add/Subtr.) Answers should be reduced
fractions or mixed numbers. If the problem had decimals, so can your answer.
8
11
 x , if x =
6)
p – 7.1, if p = 5.24
7)
14
7
-1.86
5/14
Activity:
Go over 2(1-3) Quiz
Homework:
Worksheet
Algebra One – CP 2 Chapter 2 Notes
2-6 Multiplying Rational Numbers
Rules for Multiplying with signed numbers:
 When multiplying numbers with the same sign, the product is positive.
(+)(+)=(+)
(–)(–)=(+)
 When multiplying numbers with different signs, the product is negative.
(+)(–)=(–)
(–)(+)=(–)
Recall the Multiplicative Properties:
 Multiplicative Identity Property [Mult. ID. Prop]
The product of a number and one is the number.
a1=a
* The number that is the multiplicative identity is 1.


Multiplicative Property of Zero [Mult. Prop. (0)]
The product of a number and zero is zero.
1a=a
or
0a=0
or
1
a =1
a
Multiplicative Inverse Property [Mult. Inv. Prop.]
The product of a number and its reciprocal is one.

a0=0
or
Multiplicative Property of –1 [Mult. Prop. (–1)]
The product of a number and negative one is the
opposite of the number.
a
1
=1
a
a  (-1) = (-a) or
(-1)  a = (-a)
Simplify. State T.P. ( same/diff/ Mult. ID Prop./ Mult. Prop.(0)/ Mult. Prop. (-1)
1)
(-2)(-10)
2)
(11)(-4)(2)
3)
(5)(-1)
20 same
-88 diff, diff
-5 Mult.Prop. -1
4)
(3x)(-12)
-36x diff
5)
(0.3)(5)
1.5 same
6)
(-⅞)(8)
-7 diff
7)
12  1  -4
-48 mult. ID prop., diff
8)
4⅔  ⅜
1¾
9)
(12x)(-½y)
-6xy diff
11)
| ⅔w + x |
2
12)
xy – w2
-147
Evaluate if w = -12, x = 6, y = -½
10)
10y – w
7
Activity:
I have Who has
Homework:
Worksheet
Algebra One – CP 2 Chapter 2 Notes
2-7 Dividing Rational Numbers (On Notes for LCD)
The rules for dividing signed numbers are the same as multiplying. Therefore:
 When dividing numbers with the same sign, the quotient is positive.
(+)  (+)=(+)
(–)  (–)=(+)
 When multiplying numbers with different signs, the product is negative.
(+)  (–)=(–)
(–)  (+)=(–)
The division rule says:
Division is multiplying by the reciprocal.
(You only have to use the division rule if at least one of the numbers is a fraction or if the
quotient will not be an integer.)
Simplify. Use division rule if necessary. State TP.
1)
(-32)  (-8)
2)
12  (-4)
4
-3
4)
40  ⅝
5)
64
7)
8)
6)
9)
3x + 4y
Overhead Problems
1)
(-72)  12
56  (-8)
-7
3)
(-⅔)  (-48)
1/72
4)
(6/25)/15
2/125
22x + 44
-11
4
30
-3/40
20  50 y
10
-2 + 5y
-6
2)
5)
Homework:
12 x  16 y
4
16  2
8
9
16/21
8
2
7
28
Activity:
(-⅔)  (-⅞)
3)
-2x – 4
2-7 p. 115 #14-36 Even, 2-8 p. 123 #40-50 Even
Algebra One – CP 2 Chapter 2 Notes