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Unit 9
Rational Numbers and the Coordinate Plane
Lesson 9-1 Negative Numbers in the Real World
Rational Numbers: any number positive or negative that can be written as a fraction.
Opposite: numbers that are the same distance from zero on a number line, but in opposite directions.
Positive Numbers: to the right or above zero.
Negative Numbers: to the left or below zero.
Deposit: to put in or add to.
Withdraw or Withdrawal: to take out, back away, or subtract from.
Integers: all positive and negative whole numbers or rational numbers and zero.
Origin: zero is known as origin. It’s the center point for all positive and negative numbers.
Origin
Lesson 9-2 Integers and the Number Line
Value decreases left of zero
Value increases right of zero
Lesson 9-3 Compare and Order Integers
Absolute Value: is the distance an integer is from zero. Represented by brackets │ │.
*All absolute values are positive. Examples: │3│= 3
│-15│= 15
Comparing Integers How to:
1. Negative integers are always
‹
-4 0
›
‹
less than positive integers and zero. Examples: 7
│-5│ 3
(5)
2. Small negative integers are greater than
-7
‹ -1
‹ 10
› bigger negative integers. Examples:
-3
› -15
Ordering Integers How to:
When ordering integers, pay attention to the signs and the order wanted. Least to greatest or greatest to
least.
Examples:
-8, 24, -15, 0, 1 Ordered least to greatest -15, -8, 0, 1, 24
7, -9, 1, 9, -3, -7 Ordered greatest to least 9, 7, 1, -3, -7, -9
Lesson 9-4 Integers and the Coordinate Plane
Quadrant: Coordinate Plane is divided into 4 parts called quadrants. Labeled with Roman Numerals I, II, III,
and IV
x-axis: The horizontal number line.
Always read this axis FIRST.
y-axis: The vertical number line.
Read this axis SECOND.
Origin: is zero on the number line.
Ordered pairs: the two numbers (x, y) placed on the coordinate plane.
X ,Y
Q II
Quadrant I
(- +)
A (3, 6)
B (6, 0)
C (-1, 6)
D (0, -3)
E (5, -2)
F (-4, 0)
G (-3, -4)
(+ +)
•C
•A
•F
•B
•E
•D
•G
Q IV
QIII
(+ -)
(- -)
Lesson 9-5 Rational Numbers on the Number Line
What to look for:
How is the number line divided? Is it divided into quarters, thirds, tenths, halves, wholes, etc..?
Look how the number line is labeled. Example: fractions, decimals, odds, or evens.
-2
1.75
1.5
1.25
-1
-.75
-.5
-.25
0
.25
.5
.75
1
│
│
│
│
│
│
│
│
│
│
│
│
-1 ¾
-1 ½
-1 ¼
-1
-¾
-½
-¼
0
¼
½
¾
-2
1.25
1.5
│
│
│
1
1¼
1½
1.75
│
1¾
Remember what opposite means!
Write the opposite of: -2/3 → 2/3
1 ¼ → -1 ¼
Simplifying Rational Numbers
-(-1 2/3) = 1 2/3
-(3/4) = -3/4 A negative sign outside a parenthesis means to find the opposite of what
is inside the parenthesis. The answer does NOT need parenthesis!
Lesson 9-6 Compare and Order Rational Numbers
Note: Review Lesson 9-3, before continuing on with this lesson.
Working with negative numbers, the closer to zero, the greater the value.
Watch for │ │absolute value brackets, and –( ) negative signs outside the parenthesis.
Examples: The answers are shown below each example.
≥
›3
│-5│ 3
5
│-.5│___ │ .5
›
2
5
│
1
1
4
│- │___ │- │
2
1
.4
›
2
1
│-.5│___ │- │
4
.5
4
‹
5
.8
Lesson 9-7 Rational Numbers and the Coordinate Plane
Reflected Point: The mirror image across an axis.
1.To find the distance between two points on a number line, subtract.
A
(
1 1
,
)
2 2
1 1
B (2
,
2 2
1
C ( 2, 3)
D (2
1
,
2
Distance between point A and C
)
1
3 – . Subtract the y-coordinates
2
for vertical distance. = 2
3)
1
2
units.
Distance between point A and B
2
1
2
1
- . Subtract the x-coordinates
2
for horizontal distance. = 2 units
2. Reflecting across x-axis or y-axis.
a. Across x-axis; the x-coordinate
stays the same, and the y-coordinate
goes opposite.
b. Across y-axis; the y-coordinate
stays the same, and the x-coordinate
goes opposite.
Reflect across x-axis
A (4,3) to (4, -3)
Reflect across y-axis
A (4, 3) to (-4, 3)
B (-5, -4) to (-5, 4)
B (-5, -4) to (-5, -4)