The document defines positive and negative numbers, with positive numbers being greater than zero and negative numbers being less than zero. It provides examples of how negative numbers are used to measure temperatures below zero, depths under sea level, and debt. It then explains how to add and subtract integers using a number line, with direction determined by the sign of the number. Finally, it briefly discusses multiplying integers and taking the square root of positive and negative numbers.

1. Positive and Negative Numbers
by Monica Yuskaitis

2. Definition
• Positive number – a number
greater than zero.
0 1 2 3 4 5 6

3. Definition
• Negative number – a number
less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

4. Definition
• Opposite Numbers – numbers
that are the same distance from
zero in the opposite direction
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

5. Definition
• Integers – Integers are all the
whole numbers and all of their
opposites on the negative
number line including zero.
7 opposite -7

6. Negative Numbers Are Used to
Measure Temperature

7. Negative Numbers Are Used to
Measure Under Sea Level
30
20
10
0
-10
-20
-30
-40

8. Negative Numbers Are Used to
Show Debt
Let’s say your parents bought a car but
had to get a loan from the bank for $5,000.
When counting all their money they add
in -$5.000 to show they still owe the bank.

9. Positive & Negative Numbers
Working with positive and negative
numbers is like driving in traffic.
You have to watch the traffic signs
and follow the driving rules.

10. Hint
• If you don’t see a negative or
positive sign in front of a
number it is positive.
+9

11. One Way to Add Integers Is With
a Number Line
When the number is positive count
to the right.
When the number is negative count
to the left.
- +
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

12. One Way to Add Integers Is With
a Number Line
+3 + -5 = -2
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

13. One Way to Add Integers Is With
a Number Line
+6 + -4 = +2
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

14. One Way to Add Integers Is With
a Number Line
+3 + -7 = -4
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

15. One Way to Add Integers Is With
a Number Line
-3 + +7 = +4
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

16. One Way to Add Integers Is With
a Number Line
-5 + +3 = +4
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

17. One Way to Add Integers Is With
a Number Line
-2 + +8 = +6
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

18. One Way to Add Integers Is With
a Number Line
-5 + +2 = -3
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

19. One Way to Add Integers Is With
a Number Line
-4 + -2 = -6
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

20. One Way to Add Integers Is With
a Number Line
-2 + -3 = -5
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

21. One Way to Add Integers Is With
a Number Line
-1 + -4 = -5
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

22. One Way to Add Integers Is With
a Number Line
-4 + -1 = -5
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-

23. One Way to Add Integers Is With
a Number Line
4+1= 5
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

24. One Way to Add Integers Is With
a Number Line
3+2=5
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

25. One Way to Add Integers Is With
a Number Line
1+5= 6
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+

26. Adding Integers
+9

27. Subtracting Integers
8-
8-4=
8-3=
8-2=
8-1=
8-0=
+9
8- -1=
8- -2 =
8- -3 =
8 - -4 =

28. Subtracting Integers
• Adding a negative number is the same as
subtracting a positive number.
1 + -5 = 1 - 5
• Subtracting a negative number is the same
as adding a positive number.
1 - -5 = 1 + 5

29. Multiplying Integers
8-
3x3= -3x3=
3x2= -3x2=
3x1= -3x1=
3x0= -3x0=
3x–1= -3x–1=
+9
3x–2= -3x–2=
3x–3= -3x–3=

30. What About Square Numbers
and Square Roots
5x5=
-5 x -5 =
• Therefore what could the answers be for
square root of 25?