1. The Real Number Line

2. A picture is worth 1000 words!
The real number line is a way of giving us a “picture” of the relationships among the real numbers

3. Right in the ‘middle’ of the number line, we have the origin.

4. Scale We have to choose the distance between numbers.
2 should be twice as far from 0 as 1 is!

5. Positive numbers are to the right of zero.

6. Negative numbers are to the left of zero.

7. Smaller numbers are to the left on the number line.
-2 is smaller than 0

8. The magnitude of -2 is 2 because it is 2 steps away from zero.
The magnitude of a number is just the ‘number part’ without the sign. It tells us how far the number is away from zero – but not which direction it is.
The magnitude of -2 is 2 because it is 2 steps away from zero.

9. Things are backwards in the negatives!
Magnitude
As negative numbers get smaller and smaller, their magnitude increases!
-500 is smaller than -1
Things are backwards in the negatives!

10. Inequality symbols < means ‘less than’
it looks like a tilted L (for less)

11. Inequality symbols > means ‘greater than’
(it doesn’t look like a tilted G )

12. Inserting Inequality symbols
If you have two numbers and you need to insert an inequality symbol, pretend it’s an alligator!
-2 ? 5
The alligator always has his mouth open toward the larger pile of cookies!
-2 < 5

13. Comparing 2 negatives
If the numbers that they give you are not in the order that they would be on the number line, sometimes it’s easier to draw the number line to figure out the answer.
-20 ? -45
-45
-20

14. Remember, smaller numbers are always to the left on the number line!
Comparing 2 negatives
Remember, smaller numbers are always to the left on the number line!
The number farther to the left would be -45, so the bigger pile of cookies would be the -20!
-20 > -45

15. Vocabulary
Number line
Origin
Scale
Magnitude
Inequalities