1. Critical Thinking with real numbers Uses of the “–” sign Absolute value of numbers

2. Clarification of signs
A. x + (-y) = x – y
Example: 3 + (-5) is 3 – 5 or
is 3 - 5
B. x – (-y) = x + y
Example: is or
5 –(-6) is 5 + 6
Make sure everyone is clear that I will not use “double signs”

3. The - sign Can be used interchangeably as: a minus sign as in 5 - 8
a negative sign as in -8
or as the opposite sign of a number as in –(-8) or –(8)
Make sure students are clear on this issue as that is why I won’t use double signs. See, drop the 5 before the minus and it becomes a negative sign etc.

4. Absolute Value of real numbers
Always a positive value
The distance of a number from 0
The value of an amount.
Expressed with two vertical lines.
Examples:
Discus “what does it mean to you?”

5. Practice Work inside the absolute value signs first. 6.5 –│8.8 – 10│
6.5 –│8.8 – 10│
⅞ + │¼ –⅜│
7.4 + │2 – 2.6 │
│-½ – ¾│+ ⅜

6. Review
Tell whether the equation x + ‌‌ x ‌ = 0 is always, sometimes or never true. Explain.
List the conditions under which the product of ab is negative. Give examples to support your answer.
What does this mean to you?
Think!

7. An even amount of negative numbers is multiplied
An even amount of negative numbers is multiplied. What is the sign of the product? Explain.
What is the least positive integer that is divisible by all whole #’s from 1 to 9?
What does this mean to you?
Think!

8. q2 > r2 1/q >1/r 4q > 4r Find a value for x if 1/x > x.
Determine when the statements are true for all integers q and r, where q > r.
q2 > r2
1/q >1/r
4q > 4r
What does this mean to you?
Think!

9. Which sentence is not true?
A. All natural numbers are integers.
B. Natural numbers are positive numbers.
C. Every whole number is a natural number.
D. Zero is neither positive nor negative.
Find all values for x if |x| = -|x|.
What sense do you make of this?
Think!

10. Without evaluating, can you tell between what two integers lies? Why?
What does “infinity” mean? Give examples of 2 infinite sets.
What sense do you make of this?
Think!

11. All real numbers are rational.
Is the statement below true or false? If the statement is false, give a counterexample.
All real numbers are rational.
Is the following statement true or false for all values of a and b? If false, give a counterexample.
Think!