7th grade math number system. day 1 number system, opposites & absolute value
TRANSCRIPT
7th Grade Math
Number System
Day 1Number System,
Opposites &Absolute Value
Number System
0.22
Natural1,2,3...
Whole
0
Integer
...-4, -3, -2, -1
Rational
1/5
5/2
8.3
-2.756
-3/4
1/3
-1/11
Real
Irrational
{...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...}
Definition of Integer:
The set of whole numbers, their opposites and zero.
Define Integer
Examples of Integer:
X
Definition of Rational:
A number that can be written as a simple fraction
(Set of integers and decimals that repeat or terminate)
Define Rational
0, -5, 8, 0.44, -0.23,
Examples of rational numbers:
9 , ½
X
Definition of Irrational:
A real number that cannot be written as a simple fraction
Define Irrational
Examples of irrational numbers:
X
Rational and IrrationalPerfect Squares: Rational
Imperfect Squares: Irrational
Terminating Decimals (3.89) and Repeating Decimals ( ) are rational.
Rational & Irrational Numbers
is rational because the radicand (number under the radical) is a perfect square
If a radicand is not a perfect square, the root is said to be irrational.
Ex:
Perfect Square – a number multiplied by itself. Ex: 82, 102, 132
Square Root – also called radical. a number that is multiplied by itself to form a product called a square.
Imperfect Square Root – a radical whose square root is not a whole number. Ex:
Changing a Repeating Decimal to a Fraction
to a fraction n =
Multiply both sides by 100. 100n = (100)
100n = 45. Subtract n from both sides. -n - _________________ 99n = 45Divide both sides by 99. __________________ n = 45/99
n = 5/11
Natural Numbers:
Whole Numbers:
Additive Inverse:
integer rational irrational
Classify each number as specific as possible: Integer, Rational or Irrational
5
-6
0
-21
-65
13.2
-6.32
9
2.34437 x 103
½
¾
3¾π5
-1 0-2-3-4-5 1 2 3 4 5
Rational Numbers on a Number Line
NegativeNumbers
PositiveNumbers
Numbers to the left of zero are less than zero
Numbers to the right of zero are greater than zero
Zero is neitherpositive or negative
Zero
2 Which of the following are examples of integers?
A
B
C
D
E
-5
0
-3.2
12 1 2
3 Which of the following are examples of rational numbers?
A
B
C
D
E
13
-3
10
0.25
75%
Numbers In Our World
You might hear "And the quarterback is sacked for a loss of 5 yards."
This can be represented as an integer: -5
Or, "The total snow fall this year has been 6 inches more than normal."
This can be represented as an integer: +6 or 6
Numbers can represent everyday situations
1. Spending $6.75
2. Gain of 11 pounds
3. Depositing $700
4. 10 degrees below zero
5. 8 strokes under par (par = 0)
6. feet above sea level
Write a number to represent each situation:
4 Which of the following numbers best represents the following scenario:
The effect on your wallet when you spend $10.25.
A
B
C
D
-10.25
10.25
0
+/- 10.25
5 Which of the following integers best represents the following scenario:
Earning $50 shoveling snow.
A
B
C
D
-50
50
0
+/- 50
6 Which of the following numbers best represents the following scenario:
You dive feet to explore a sunken ship.
A
B
C
D
0
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
The numbers -4 and 4 are shown on the number line.
Both numbers are 4 units from 0, but 4 is to the right of 0 and -4 is to the left of zero.
The numbers -4 and 4 are opposites.
Opposites are two numbers which are the same distance from zero.
Opposites
7 What is the opposite of -7?
8 What is the opposite of 18.2?
What happens when you add two opposites?
Try it and see...
A number and its opposite have a sum of zero.
Numbers and their opposites are called additive inverses.Click to Reveal
• An integer is a whole number, zero or its opposite.
• A rational number is a number that can be written as a simple fraction.
• An irrational number is a number that cannot be written as a simple fraction.
• Number lines have negative numbers to the left of zero and then positive numbers to the right.
• Zero is neither positive nor negative.
• Numbers can represent real life situations.
To Review
X
Absolute Value of Numbers
The absolute value is the distance a number is from zero on the number line, regardless of direction.
Distance and absolute value are always non-negative (positive or zero).
10 2 3 4 5 6 7 8 9 10-1-2
-3-4-5-6-7-8-9-10
What is the distance from 0 to 5?
10 2 3 4 5 6 7 8 9 10-1
-2-3-4-5-6-7-8-9-10
What is the distance from 0 to -5?
10 2 3 4 5 6 7 8 9 10
-1-2
-3
-4
-5-6-7
-8
-9
-10
Absolute value is symbolized by two vertical bars
|4|
What is the | 4 | ?
This is read, "the absolute value of 4"
|-4| = 4
|-9| = 9
= 9.6|9.6|
Use the number line to find absolute value.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
Moveto check
Move to
check
Moveto check
14 Find
15 Find |-8|
Treat Absolute Value Symbols as parenthesis.
Examples: a)
b)
c)
17 What is ?
18 Find
A
B
C
D
E
-30
-15
0
15
30
20 Which numbers have 15 as their absolute value?
A
B
C
D
E
-100
-50
0
50
100
21 Which numbers have 100 as their absolute value?