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Positive and Negative Numbers
Definition
Rational Numbers – numbers that
can be expressed as one integer a
divided by another integer b,
where b is not zero
You can write a rational number
a
in the form
or in decimal
b
form
Definition
• Positive number – a number
greater than zero.
0 1 2 3 4 5 6
Definition
• Negative number – a number
less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Definition
• Opposite Numbers – numbers
that are the same distance from
zero in the opposite direction
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Definition
• Integers – Integers are all the
whole numbers and all of their
opposites on the negative
number line including zero.
7
opposite
-7
Hint
• If you don’t see a negative or
positive sign in front of a
number it is positive.
+9
Inequalities and their Graphs
Objective:
To write and graph simple
inequalities with one variable
Inequalities and their Graphs
What is a good definition for Inequality?
An inequality is a statement that
two expressions are not equal
2
3
4
5
6
7
8
Inequalities and their Graphs
Terms you see and need to know to graph inequalities correctly
< less than
> greater than
Notice
open
circles
Inequalities and their Graphs
Terms you see and need to know to graph inequalities correctly
≤ less than or equal to
≥ greater than or equal to
Notice colored in circles
Inequalities and their Graphs
Let’s work a few together
x>3
Notice: when variable is on
left side, sign shows
direction of solution
3
Inequalities and their Graphs
Let’s work a few together
x<7
Notice: when variable is on
left side, sign shows
direction of solution
7
Inequalities and their Graphs
Let’s work a few together
p £ -2
Notice: when variable is on
left side, sign shows
direction of solution
-2
Color in
circle
Inequalities and their Graphs
x³8
Color in circle
Notice: when variable is on
left side, sign shows
direction of solution
8
Ordering fractions
If the DENOMINATOR is the same, look at the
NUMERATORS, and put the fractions in order.
1
2
3
4
7
9
9
9
9
9
(if ordered smallest
largest)
Ordering fractions
If the DENOMINATOR is the different, we have a
problem that must be dealt with differently.
3
7
4
1
2
6
8
4
3
4
We need to convert our fractions to EQUIVALENT
fractions of the same DENOMINATOR. We will
come back to this example.
Ordering fractions
If the DENOMINATOR is different, we have a
problem that must be dealt with differently.
4
3
6
9
Here’s an easier example, with just 2
fractions to start us off.
Ordering fractions
Look at the denominators. We must look for a
COMMON MULTIPLE.
4
3
6
9
This means that we check to see which numbers
are in the 6 times table, and the 9 times table. We
need a number that appears in both lists.
Homework
Page 20-21, #’s 5, 9-19 ODD, 20-21
Page 22-23, #’s 24-44 EVEN,
Page 26, #76-77
Page 27, #78-84 EVEN, 85-87