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Section 2.1
Real #s and Absolute Value
Algebra I
Pass Skills 1.2a
Obj: Compare real #s
Obj: simplify expressions involving opposites and absolute value.
Vocab
absolute value  the distance of a # from 0.The symbol |x| means
the absolute value of x.
Integers  …-3,-2,-1,0,1,2,3,….
irrational numbers neither repeating or terminating decimal
natural numbers 1,2,3,4,….
negative numbers  < 0
Opposites opposite sides of a # line.
positive numbers
>0
rational numbers a/b, fractions
real numbers rational & irrational #’s
Whole 0,1,2,3,…
Compare values of real numbers.
Insert an ordering symbol to make each
statement true.
a.
5
–12
b.
9
a.
5 is to the right of –12 on a number line, so
5 > –12.
b.
9 is to the left of 17 on a number line, so
9 < 17.
17
Find the absolute value of a number.
To find the absolute value of –11, find the distance
from –11 to 0 on a number line.
|–11| = 11
Section 2.2
Adding Real #s
Pass Skills1
Obj: add #s with like signs.
Obj: add #s with unlike signs.
Vocab
Additive Inverse Property  for every real # a there is exactly on real # -a
additive inverses  any # plus its opposite = 0
Identity Property for Addition  any # + 0 = that number
Rules for Adding Two Signed Numbers
A. Like signs:
Find the sum of the absolute values.
Use the sign common to both numbers.
B. Unlike signs:
Find the difference of the absolute values.
Use the sign of the number with the greater absolute value.
Identity Property for Addition
For all real numbers a, a + 0 = a and 0 + a = a.
Additive Inverse Property
a + (–a) = 0 and –a + a = 0
Add two or more real numbers.
Example 1:
–15 + (–37)
–15+–37= 52
–15 + (–37) = –52
Algebra I
Example 2:
16 + (–29)
–29–16= 13
–29>16
16 + (–29) = –13
Section 2.3
Subtracting Real #s
Algebra I
Pass Skills 1
Obj: define subtraction in terms of addition.
Obj: subtract Is with llike and unlike signs.
Vocab
Closure property  a set of #s is said to be closed, or to have closure, under a given operation if the
result of the operation on any 2 #s in the set is also in the set.
Subtraction  For all real #s a and b, a-b=a+(-b)
Subtract real numbers.
To subtract a number, add its opposite.
Example 1:
–51 – 17 = –51 +(–17) = –68
Example 2:
–22 – (–3) = –22 + 3 = –19
Section 2.4
Multiplying and Dividing Real #s
Algebra I
Pass Skills 1
Obj: multiply and divide positive and negative #s.
Obj: define the properties of zero.
Vocab
Identity property for multiplication for all real #s a, a x 1 = a.
Multiplicative inverse  reciprocal
Multiplicative inverse property  for every nonzero real # a, there is exactly one # 1/a such that a x 1/a
=1 and 1/a x a =1
Properties of zero  let a represent any #.
1. The product of any # and zero is zero
2. Zero divided by any nonzero # is zero
3. Division by zero is undefined. (not possible)
Rules and Properties
Multiplying Two Numbers With Like Signs
(+)  (+) = (+)
(–)  (–) = (+)
Multiplying Two Numbers With Unlike Signs
(+)  (–) = (–)
(–)  (+) = (–)
Dividing Two Numbers With Like Signs
(+) ÷ (+) = (+) (–) ÷ (–) = (+)
Dividing Two Numbers With Unlike Signs
(+) ÷ (–) = (–)
(–) ÷ (+) = (–)
Multiply and divide real numbers.
Find each product or quotient.
a. (–25)(–3)
(–)  (–) = (+)
|–25| |–3|
(–25)(–3) = 75
b. 128 ÷ (–8)
(+) ÷ (–) = (–)
|128| ÷ |–8|
128 ÷ (–8) = –16
Section 2.5
Properties and Mental Computation
Algebra I
Pass Skills 1
Obj: State and apply the commutative, associative, and distributive properties.
Obj: use the commutative, associative, and distributive properties to perform mental computations.
Vocab
Commutative Property of Addition
a+b=b+a
Commutative Property of Multiplication
ab=ba
Associative Property of Addition
(a + b) + c = a + (b + c)
Associative Property of Multiplication
(a  b) c = a (b  c)
Distributive Property of Multiplication over Addition and Subtraction:
For all numbers a, b, and c.
a(b + c) = ab + ac
(b + c)a = ba + ca
a(b – c) = ab – ac
(b – c)a = ba – ca
Reflexive Property of Equality:
a = a (A number is equal to itself.)
Symmetric Property of Equality:
If a = b, then b = a.
Transitive Property of Equality:
If a = b and b = c, then a = c.
Substitution Property of Equality:
If a = b, then a and b are interchangeable.
Simplify:
a. (37 + 89) + 11
Use the Associative Property.
37 + (89 + 11)
37 + 100
137
b. (25  13)  4
Use the Commutative Property.
(13  25)  4
Use the Associative Property.
13  (25  4)
13  100
1300
To find the opposite of an expression multiply everything by a -1.
Section 2.6
Adding and Subtracting Expressions
Algebra I
Pass Skills 1.2b
Obj: use the distributive property to combine like terms.
Obj: simplify expressions with several variables.
Vocab
Coefficient  a # that is multiplied by a variable.
Like terms  terms that contain the same form of a variable.
Simplified  an algebraic expression is said to be simplified when all of the like terms have been
combined and all parentheses have been removed.
Term  each # in a # sequence; a #, a variable, or a product or quotient of #s and variables that is added
or subtracted in an algebraic expression.
Add and subtract expressions, and combine like terms.
Add (5a + 7b) + (7a +12b).
5a + 7b + 7a + 12b
(5a + 7a) + (7b + 12b)
12a + 19b
Add and subtract expressions, and combine like terms.
Subtract (15x + 8) – (9x + 4).
15x + 8 + (–9x – 4)
[15x + (–9x)] + [8 + (–4)]
6x + 4
Section 2.7
Multiplying and Dividing Expressions
Algebra I
Pass Skills 1.2b
Obj: multiply expressions containing variables.
Obj: divide expressions containing variables.
Vocab
Base (of a power)  the # that is raised to an exponent. In an expression of the form x2, x is the base.
Exponent  in a power, the # that tells how many times the base is used as a factor. In an expression of
the form xa, a is the exponent.
Power  an expression of the form xa, where x is the base and a is the exponent.
Dividing an Expression
Multiply and divide expressions.
a. –3(2z + 7)
–3(2z) + (–3)(7)
–6z – 21
b. (5x + 9) – 2(x + 3)
(5x + 9) –2(x) + (–2)(3)
5x + 9 – 2x – 6
3x + 3
4k2 + k + 9