Download Lesson 2, Section 1

Lesson 2-3, Section 1.2
A
Absolute Value
Definition: The absolute value of a is the distance (number of units)
a
between 0 and a.
 7.4 
2
1
3
5


52

5
 
0
B
Inequalities
Number Line: A number to the left of a given number is less than the given
number. A number to the right of a given number is greater than the given number.
-10
-6
-8
-4
-2
0
2
4
6
8

less than
25

greater th an
 4  10

less than or equal to
25

2  5 or 2  5

greater th an or equal to
00

0  0 or 0  0
10
Write or state the meaning. Determine True or False.
1.  4.6  0
2.  12  8
3. 4  4
4.  3  3
5. 2  2
1
1
3
6
6. 4.5  4
2
3
7. 4  2
8. 12  2
1
Write as an inequality.
1. Five is less than or equal to seven
2. Twelve is greater than negative one
3.
C
Addition and Subtraction of Rational Numbers
Laws of Inverses:
a  (a)  0
Additive inverse or Opposites:
Multiplicative inverses or Reciprocals: a 
1
a
1
 (a)  a
Double Negative Rules:
a
a
1
Never use ‘double signs’. Always rewrite the arithmetic problem without double signs.
5  ( 6 )  5  6
 1  ( 2 ) 
5  2
   
4  3
To Add or Subtract two rational numbers:
1. Eliminate any ‘double signs’.
2. If both number are plus (positive) or both minus (negative)
a) Add the absolute values of the numbers.
b) Use the same sign.
3. If the numbers have opposite signs:
a) Find the difference of the absolute values.
b) Use the sign of the larger absolute value.
1)
 12  (6) 
2)
 4.34  6.2 
3)

4 1
 
3 6
4)
6  6 
5)
6 10 
6)

4 1
 
13 2
2
7)
 8.14  4.5 
9)

4 2 1
  
5 3 2
8)
4.6  4.5  10.8  2 
10)
 8  12  20  2  18 
Given x, find  x . Note:  x does not always denote a negative value.
x  12
x
3
4
x
x
x  1.25  x 
D
Multiplication and Division of Rational Numbers
Write the reciprocals of each. Note: Reciprocals have the same sign.
2
4
3
4
2
3
4.6
*4.6 
46
?
10
To Multiply or Divide two rational numbers:
1. Multiply or Divide the absolute values.
2. If the two numbers have the ‘same’ sign, the answer is positive.
3. If the two numbers have ‘different’ signs, the answer is negative.
4. If there are more than two numbers, count the number of negatives. If odd, the
answer is negative; if even, the answer is positive.
a a
a

5. With fractions,  
b
b
b
n
 12
is undefined; for example
is undefined
0
6. 0
0
0
 0 ; for example  0
n
6
3
1)
(6)( 4)( 8) 
2)
7  1
   
8  2
3)
 3.1 6 
4)
2 1
  2  
3 7
5)
 24

6
6)
1.288  0.23 
E
Order of Operations with Rational Numbers
1. Work within groupings (parentheses) first.
2. Evaluate all exponents next.
3. Perform multiplication and/or division, left to right.
4. Perform addition and/or subtraction, left to right.
4
Note:  2 4 (2)(2)(2)(2)  16
(2)  (2)(2)(2)(2)  16
1)
4  (2  3 )
2 2
2)
4  5(2)  7
4 2  2(5)
=
=
3)
8  4  6  42  5
=
4
4)
8
(6)  4
4
100  4(5) 2
5)
4  (1  9)2  6  22  8
=
=
2
6)
 2   4  25   1 1 
         
 3   5  24   3 6 
=
5
F
Distributive Property
a(b  c)  ab  ac 0R
ab  ac  a(b  c)
Note: The second part of the property above is commonly called factoring out the
greatest common factor.
Write an equivalent expression using the distributive property.
4( x  2) 
1)
2)
2( x  y  8) 
3)
5 x( y  z  w) 
4)
m[ x  3(a  4)] 
Find an equivalent expression by factoring.
1)
7a  14 
2)
ab  39b 
6