1. 7th Grade Math
Number System

2. Day 1
Number System,
Opposites &
Absolute Value

3. Number System Real Rational 1/3 Integer 5/2 Whole 0.22 Irrational
Natural
1,2,3...
Whole
Integer
...-4, -3, -2, -1
Rational
1/5
5/2
8.3
-2.756
-3/4
1/3
-1/11
Real
Irrational

4. X Define Integer Definition of Integer:
The set of whole numbers, their opposites and zero. X
Examples of Integer:
{...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...}

5. X Define Rational Definition of Rational:
A number that can be written as a simple fraction
(Set of integers and decimals that repeat or terminate) X
Examples of rational numbers: 9
, ½
0, -5, 8, 0.44, -0.23,

6. X Define Irrational Definition of Irrational:
A real number that cannot be written as a simple fraction X
Examples of irrational numbers:

7. Rational and Irrational
Perfect Squares: Rational
Imperfect Squares: Irrational
Terminating Decimals (3.89) and Repeating Decimals ( ) are rational.

8. 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:

9. 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:

10. Changing a Repeating Decimal to a Fraction
to a fraction n =
Multiply both sides by n = (100)
100n = 45.
Subtract n from both sides n
_________________
99n = 45
Divide both sides by 99.
__________________
n = 45/99
n = 5/11

11. Natural Numbers:
Whole Numbers:
Additive Inverse:

12. Classify each number as specific as possible: Integer, Rational or Irrational
3.2 -6
-21 1 5 π 9 5 3¾
-65
-6.32
x 103
integer
rational
irrational

13. Rational Numbers on a Number Line
Negative
Numbers
Positive
Numbers
Zero -5 -4 -3 -2 -1 1 2 3 4 5
Numbers to the
left of zero are
less than zero
Zero is neither
positive or negative
Numbers to the right of zero are greater than zero

14. Which of the following are examples of integers?2
Which of the following are examples of integers? A -5 B C
-3.2 D 12 1 2 E
Answer: A, B, D

15. Which of the following are examples of rational numbers?3
Which of the following are examples of rational numbers? 1 3 A B -3 C 10 D
0.25 E
75%
Answer: A, B, C, D, E

16. Numbers In Our World

17. Numbers can represent everyday situations
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

18. Write a number to represent each situation:
Spending $6.75
Gain of 11 pounds
Depositing $700
10 degrees below zero
8 strokes under par (par = 0)
feet above sea level

19. Which of the following numbers best represents the following scenario:4
Which of the following numbers best represents the following scenario:
The effect on your wallet when you spend $10.25. A
-10.25 B
10.25 C D +/
Answer: A

20. Earning $50 shoveling snow.
Which of the following integers best represents the following scenario:
Earning $50 shoveling snow. A
-50 B 50 C D
+/- 50
Answer: B

21. Which of the following numbers best represents the following scenario:6
Which of the following numbers best represents the following scenario:
You dive feet to explore a sunken ship. A B C
Answer: A D

22. Opposites The numbers -4 and 4 are shown on the number line. 1 2 3 4 52 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
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.

23. 7 What is the opposite of -7?
Answer: 7

24. 8
What is the opposite of 18.2?
Answer: -18.2

25. What happens when you add two opposites? Try it and see...
Click to Reveal
A number and its opposite have a sum of zero.
Numbers and their opposites are called additive inverses.

26. X To Review 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.

27. 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). 1 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? 1 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?

28. Absolute value is symbolized by two vertical bars
|4|
This is read, "the absolute value of 4" 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10
What is the | 4 | ?

29. Use the number line to find absolute value.
Move to
check
|9.6| =
9.6
Move
to check
|-9| = 9
Move
to check
|-4| = 4 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9
-10

30. 14
Find
Answer: 56

31. 15
Find |-8|
Answer: 8

32. Treat Absolute Value Symbols as parenthesis. Examples: a) b) c)
Answer: 7.3

33. 17
What is ?
Answer: 22 3/5

34. 18
Find
Answer: …

35. Which numbers have 15 as their absolute value?20
Which numbers have 15 as their absolute value? A
-30 B
-15 C D 15 E 30
Answer: B, D

36. Which numbers have 100 as their absolute value?21
Which numbers have 100 as their absolute value? A
-100 B
-50 C D 50 E
100
Answer: A, E