Download ALesson Ch 2

Lesson #2-1 – Adding Rational Numbers
Use number line to simplify each
expression.
Identity Property of Addition – For
every real number n, n + 0 = n and
0 + n = n.
1. 3 + (–5)
Inverse Property of Addition – For
every real number n, there is an additive inverse –n such that n + (–n) = 0.
2. –3 + 5
3. ( –3) + ( –5)
Simplify each expression.
Adding Integers –
1) When the signs are the same, add
and keep the same sign.
–2+–6=–8
4. 12 + ( –23)
5. –6.4 + ( –8.6)
2) When the signs are different,
subtract, and keep the sign of the
biggest absolute value.
–2+6=–4
6. The water level in the lake rose 6
inches and then fell 11 inches.
Evaluate expressions – remember to
Write an addition statement to
use parenthesis.
find the total change in water
level.
Matrix – a rectangular arrangement
of numbers in rows and columns.
Plural = matrices
7. Evaluate 3.6 + ( –t) for t = –1.7.
 6
8. Add 
2.3
7
11.1

8.6 11 
+
5
 3
 5.4 2 
3
 1
 5   9  4
 3 .2     1 .7    1 .5 

 
 

  4.9   11.1   16
Element – each item in a matrix.
Prentice Hall - Algebra 1 (2007)
Lesson #2-2 – Subtracting Rational Numbers
1. Find –3 – 2 using a number line.
Subtracting Integers – Instead of
subtract, add the opposite.
–4 – ( –9) = –4 + 9 = 5
2. Find 4 – ( –2).
Absolute Value – Distance from zero.
| 5 – 11| = | –6| = 6
3. –11.6 – ( –14)
Evaluate – remember to use
parenthesis.
4.
2  4
 
3  9
5. | –13 – ( –21)|
6. Evaluate x – ( –y) for x = –3 and
y = –6
7. The temperature in Montreal,
Canada at 6:00 pm was –8F.
Find the temperature at 10:00 if
it fell 7F.
Prentice Hall - Algebra 1 (2007)
Lesson #2-3 – Multiplying and Dividing Rational Numbers
1. –3 ( –11)
Identity Property of Multiplication –
For any number n, 1  n = n.
 3
2. –6  
 4
Multiplication Property of Zero – For
any number n, n  0 = 0.
3. Evaluate 5rs for r = –18 and
s = –5.
 a 
4. Use the expression –5.5 

 1000 
to calculate the change in
temperature for an increase in
altitude of 7200 ft.
5. –0.24
6. ( –0.2)4
7. 70  ( –5)
Multiplication Property of –1 – For
any number n, n  –1 = –n.
Multiplying Integers –
1) A negative times a negative is a
positive.
2) A negative times a positive is a
negative.
–4( –6) = 24
–4( 6) = –24
Simplifying Exponential Expressions
– If the base is inside parenthesis and
the exponent is even, the answer will
be positive. If the exponent is odd,
the answer will be negative.
( –5)2 = 25
( –5)3 = –625
–52 = –25
**** If the base is not inside
parenthesis, then the negative is not
“tied” to the number and is separate.
8. –54  ( –9)
Prentice Hall - Algebra 1 (2007)
Lesson #2-4 – The Distributive Property
1. Use the Distributive Property to Distributive Property – For every
simplify each expression 26(98). real number a, b, and c,
a( b + c) = ab + ac
34(102) = 34(100 + 2) =
3400 + 64 = 3464
2. Find the total cost of 4 CDs that
cost $12.99 each.
2( 5x + 3) = 10x + 6
**** Note: When using the distributive
property in algebraic expressions, the
answer will have the same number of
terms as there are inside the parenthesis.
3. Simplify 3( 4m – 7).
– ( 6s + 4) = – 6s – 4
This expression has 3 terms
–2x + 16 + x
4. Simplify – ( 5q – 6).
-2 is the coefficient
1 is the coefficient
Like terms – contain the same
variable.
5. Simplify – 2w2 + w2
Constant – a term without a variable.
Like terms
4a + 5 + 3a + 9
6. Write an expression for “the
quantity of –6 and the quantity 7
minus m.”
Constants and like terms
7a + 14
Simplest Form- an algebraic
expression that has no like terms and
no parenthesis.
Simplifying the Expression – using
distributive property and adding like
terms.
Prentice Hall - Algebra 1 (2007)
Lesson #2-5 – Properties of Numbers
Name the property that each
equation illustrates.
Copy Property Box p 86.
1. 1m = m
2. ( –3 + 4) + 5 = –3 + (4 + 5)
3. – 14  0 = 0
4. Give a reason to justify each
step.
a. 3x – 2(x + 5) = 3x – 2x – 10
b. = 3x + (–2x) + (–10)
c. = [3 + (–2)]x + (–10)
d. = 1x + (–10)
e. = 1x – 10
f. = x – 10
Prentice Hall - Algebra 1 (2007)
Lesson #2-6 – Theoretical and Experimental Probability
Use number line to simplify each
expression.
1.
2.
3.
4.
5.
6.
7.
8.
Lesson #2-7 – Probability of Compound Events
Use number line to simplify each
expression.
1.
Prentice Hall - Algebra 1 (2007)
2.
3.
4.
5.
6.
7.
8.
Prentice Hall - Algebra 1 (2007)