Download Algebra 2-1 Integers and the Number Line A. Graph rational

Algebra 2-1 Integers and the Number Line
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
A. Graph rational numbers
1. Integers are positive or negative whole numbers.
2. A rational number is a number that can be
a
written in the form .
b
3. To graph a set of numbers means to draw, or plot
the points named by those numbers on a number line.
Ex 1: Name the set of numbers graphed.
-9
-8 -7 -6
-5 -4 -3
-2
-1
0
1
2
3
4
5
6
7
8
9
4
5
6
7
8
9
{0, 1, 2, 3, 4}
Ex 2: Graph {…, -9, -8, 0, 4, 5, 6}
-9
-8 -7 -6
-5 -4 -3
-2
-1
0
1
2
3
B. Absolute value
1. The absolute value of a number is its distance
from zero on the number line.
Ex 3: Find each absolute value.
2
a.) −4 = 4
b.) = 2
3 3
HW: Algebra 2-1 p. 71-72
19-41 odd, 42-44, 45-55 odd, 61-65, 67-77 odd
Section 2-2 Adding and subtracting Rational Numbers
A. Add and Subtract Rational Numbers
1. Adding rational numbers is just like adding
regular numbers, except watch for the signs.
Ex 1: Find the sum or difference.
a.) 12 + 14= 26 b.) 39 + (−22) =17
c.) −28 + 16 = -12 d.) −7 − 14 = -21
2. When adding or subtracting fractions (rational
numbers) make common denominators.
Ex 2: Find the sum or difference.
2 8
3 5
a.) −
b.) − −
3 9
5 4
23 8
=  −
33 9
6 8
= −
9 9
2
=−
9
3 4  5 5
=−  −  
5 4  4 5
−12 25
=
−
20 20
HW: Algebra 2-2 p. 76-78
17-55 odd, 57-59, 65-69, 73-81 odd
Section 2-3 Multiplying Rational Numbers
A. Multiplying Integers
1. The product of two negative numbers is positive.
2. The product of a positive and negative number is
negative.
Ex 1: Find the products.
a.) 6(−4) = -24
b.) 2(3)(−5) = -30
Ex 2: Simplify
a.) 2(−5 x) − 3x
= −10 x − 3x
= −13x
B. Multiply rational numbers
1. Make sure to reduce when possible.
Ex 3: Find the products
2 4
3  1  3 
a.)  −  = −8
b.) −   −  =
3  5  15
5  4  2 
9
40
Section 2-4 Dividing Rational Numbers
A. Divide Integers
1. Two negative numbers gives a positive quotient.
2. A positive and negative number gives a negative
quotient.
Ex 1: Find each quotient
a.) 44 ÷ ( −4) = -11
b.)
−70
= 10
−7
B. Divide Rational Numbers
1. You must multiply by the reciprocal.
Ex 2: Find each quotient
3  −3 
2  −4 
a.) ÷   =
b.) − ÷   =
8  5 
15  5 
3 −5
= ⋅
8 3
5
=−
8
Ex 3: Simplify
12 x + 4
a.)
2
=
12 x 4
+
2
2
= 6x + 2
HW: Algebra 2-3 p. 81-82
17-39 odd, 43-49 odd
Algebra 2-4 p. 86-87
17-43 odd, 47-51 odd, 60-73
−2  −5 
⋅ 
15  4 
1
=
6
=
b.)
15r − 12
3
=
15r 12
−
3
3
= 5r − 4
Section 2-6 Simple Probability and Odds
A. Probability
1. The probability of a simple event is the number
of favorable outcomes divided by total outcomes.
Ex 1: Find the probability of:
a.) flipping a coin and getting heads. =½
b.) rolling a die and getting a 5. = 1/6
c.) pulling a queen out of a standard deck of 52 cards.
=1/13
B. Odds
1. The odds of an event happening is the favorable
outcomes over the non-favorable outcomes.
Ex 2: Find the odds of:
a.) rolling a die and getting a number less than 3.
=
2 1
=
4 2
b.) picking an ace out of a deck of cards.
=
HW
4
1
=
48 12
HW: Algebra 2-6 p. 99-101
15-21 odd, 29-47 odd, 50, 62, 65-81 odd
Algebra 2-7 Square roots and real numbers
A. Square roots
1. A square root is two equal factors of a number.
2. A number like 64, whose square root is a rational
number is called a perfect square.
Ex 1: Find each square root.
16
a.) 25 = 5
b.)
49
c.) − 225
16 4
=
49 7
=
1
100
c.) ±
= −15
=±
1
1
=±
10
100
Ex 2: Classify each number as rational or irrational,
then determine if it is an integer.
a.) 289
b.) 3
=17 rational
=integer
=irrational
Ex 3: Graph each solution set.
a.) x > −3
-9
-8 -7 -6
-5 -4 -3
-2
-1
HW: Algebra 2-7 p. 107-109
0
1
2
3
4
5
6
7
8
9
20-31, 33-49 odd (like ex 2) 50, 52-54, 78-79, 80-83, 85-88