Transcript UNIT II Algebra 1 - Sections 2.2, 2.3, & 2.5

The set of all numbers that can be represented on
a number line are called real numbers. You can
use a number line to help you with addition and
subtraction of real numbers.
Addition
To add a number, always move to the right.
Subtraction
To subtract a number, always move to the left.
BUT:
If adding or subtracting a NEGATIVE number,
switch directions.
Add or subtract using a number line.
–3 + 7
Start at 0. Move left to –3.
To add 7, move right 7 units.
+7
–3
-3 -2 -1 0 1 2 3 4 5 6 7 8 9
–3 + 7 =
4
Add or subtract using a number line.
–4 + (–7)
+ (–7)
Start at 0. Move left to –4.
To add –7, move left 7 units.
11 10 9 8 7 6 5 4 3
–4 + (–7) =
–11
–4
2 1 0
Add or subtract using a number line.
3 – (–6)
Start at 0. Move right to 3.
To subtract –6, move right 6 units.
–(–6)
+3
-3 -2 -1 0 1 2 3 4 5 6 7 8 9
3 – (–6) =
9
Add or subtract using a number line.
–3 – 7
Start at 0. Move left to –3.
To subtract 7, move left 7 units.
–7
–3
11 10 9 8 7 6 5 4 3 2 1 0
–3 – 7 = –10
Subtracting can be thought of as the “opposite of”.
5 – (–4)
5 − (–4) = 5 + 4
5−
(5 (–
+44) = 5
9)+ 4
=9
To subtract –4, add 4.
Add or subtract using a number line.
–5 – (–6.5)
Start at 0. Move left to –5.
To subtract –6.5, move right
6.5 units.
– (–6.5)
–5
8 7 6 5 4 3 2 1 0 1 2
–5 – (–6.5) =
1.5
Another way to look at it:
a) 7 + 12
So, try some now:
b) –2 – 9
1)
c)
d)
6 – (–8)
–5 + 8
e)
5 - 14
–13 – 4
2)
10 – (-9)
3)
–11 + 6
4)
2 +(-13)
Chapter 2.3 and 2.4 –
Multiplying and Dividing
Rational Numbers
When you multiply or divide two numbers, the signs of the
numbers determine whether the result is positive or negative.
Numbers
Product/Quotient
Both positive
Positive
One negative
Negative
Both negative
Positive
Find the value of each expression.
A.
C.
–5
B.
12
a.) 4(-3y) – 15y
-12y – 15y
-27y
b.) 13x + (-6)(4x)
13x + (-24x)
-11x
Stock Market Example
500,000 (1.25) = $625,000 DROP!!
Two numbers are reciprocals if their product is 1.
A number and its reciprocal are called multiplicative inverses.
To divide by a number, you can multiply by its
multiplicative inverse.
Evaluate the expression.
Example 2 Dividing by Fractions
Helpful Hint
You can write the reciprocal of a number by
switching the numerator and denominator. A
number written without a denominator has a
denominator of 1.
Evaluate the expression
a.)
15a 10
5
b.)
36 x  24
3
15a 10

5
5
36 x  24
(
)
3
3
3a + 2
– 12x + 8
Lesson Review
Simplify.
a. -8 + 13
b. 7 – 19
c. -12 – (-15)
d. -10 + (-36)
e.
 90h
10
f.
40 x  10
5
g.
2
 14
3
h.
3
  (6)
5

2-2, 2-3 & 2-4 Study Guide/Skills Practice
Worksheets (In-Class)
Homework
 Pages 823 – Lesson 2-2 Odds
 Pages 823 – Lesson 2-3 Odds
 Pages 824 – Lesson 2-4 Odds

Quiz on Sections 1-1, 1-2, 1-5, 2-2, 2-3,
and 2-4 on Friday, September 18th!!!