2. real rational irrational rational Real Numbers
All numbers are numbers. There are two types of real numbers; they are numbers and numbers. Natural numbers, whole numbers, integers are all numbers.
rational
irrational
rational

3. Adding Integers
We can use positive and negative counters to model the addition of integers.
Positive Integer
Negative Integer
A positive integer paired with a negative integer form a zero pair. The value of a zero pair is 0.

4. Add -2 + (-4)
= -6

5. Add 5 + 6
= 11

6. Add -3 + (-5)
= -8

7. Add
= -5

8. Do you notice a pattern or rule?
Adding Integers with like signs.
- When the signs are the same, add the numbers together and keep the sign.

9. Add
= -2
Remove all the zero pairs.

10. Add 4 + (-1)
= 3
Remove all the zero pairs.

11. Add
= -1
Remove all the zero pairs.

12. Add 3 + (-7)
= -4
Remove all the zero pairs.

13. Did you notice a pattern or rule?
Adding integers with unlike signs.
- When the signs are different, subtract the integers and keep the sign of the larger digit.

14. Summary Adding Integers with like signs.
- When the signs are the same, add the numbers together and keep the sign.
= -12
Adding integers with unlike signs.
- When the signs are different, subtract the integers and keep the sign of the larger integer.
= -6

15. Let’s try a few examples using the rules for adding integers.
1) =
2) =
3) (-19) =
4) =
5) =
6) (-16) =
7) (-5) =
-20 -6 12 -2
-38 13

16. −6 14 + −4 14 = Simplify. −7 11 + 2 11 = −𝟕+𝟐 𝟏𝟏 = −𝟔+−𝟒 𝟏𝟒 = −𝟓 𝟏𝟏
Class Review
First and Last Name
November 29, 2017
Simplify.
− =
− −4 14 =
−𝟓 𝟏𝟏
−𝟕+𝟐 𝟏𝟏 =
−𝟔+−𝟒 𝟏𝟒 =
−𝟏𝟎 𝟏𝟒
÷ 2
−𝟓 𝟕
÷ 2

17. Rule for subtracting integers
To subtract integers, add the opposite.
What does this mean?
Keep, Change, Change
Keep the 1st integer the same
Change the subtraction sign to addition.
Change the sign of the second integer.
Then follow the rules for addition.

18. Let’s try an example.
-5 – (-2)
keep, change, change
Opposite sign subtract and keep the sign of the larger digit.
= -3

19. Let’s try an example
-4 – 3
-4 + (-3) keep, change, change
Same sign add the integers and keep the sign.
-4 + (-3) = -7

20. 10 Example + 6 – (-4) 6 4 Keep, Change, Change
Now follow the rules for adding integers! 10

21. -13 Example + -5 – 8 -5 -8 Keep, Change, Change
Now follow the rules for adding integers!
-13

22. -2 Example + 18 – 20 18 -20 Keep, Change, Change
Now follow the rules for adding integers! -2

23. Time for some practice! -9 + -5 = -14 -9 – 5 = 27 – (-8) = -3 – (-1) =
-8 – 9 =
14 – 17 =
4 – (-19) = 35 = = -2 =
-17 = -3 = 23

24. Rewrite as an addition problem then solve.
5 – (-4) =
-7 – (-8) =
2 – 6 =
-12 – 12 =
-14 – (-14) =
5 + 4 = 9 = 1 = -4 =
-24 =

25. -2 – 3 -2 + – 3 Subtraction Addition
Ex 1a: Write an equivalent subtraction and addition expressions for the model below. • •
Subtraction -2
– 3 -2
+ – 3
Addition

26. 3 – 4 3 + – 4 Subtraction Addition
Ex 1b: Write an equivalent subtraction and addition expressions for the model below. • •
Subtraction 3
– 4 3
+ – 4
Addition

27. 8 – 10 = 8 + -10 = – 2°F – 7°F – 2 – 5 = – 2 + -5 = Temp at 5:00 P.M.
Ex 2a:
Between 6:00 A.M. and noon, the temperature rose from 0°F to 8°F. By 5:00 P.M., the temperature had dropped by 10°F. By 8:00 P.M., the temperature dropped another 5°F. Write and simplify a subtraction expression for the temperature at 5:00 P.M. and 8:00 P.M.
Temp at 5:00 P.M. 8
– 10 = =
– 2°F
Temp at 8:00 P.M.
– 7°F
– 2
– 5 =
– =

28. Ex 3: Rewrite as an addition problem then solve.
To subtract an integer, add it’s opposite.
Keep, Change, Change
6 – (-1) = =
-4 – (-3) = =
1 – 6 = =
-3 – (-4) = =
-3 – 5 = = 6 1 7 -4 3 -1 1 -6 -5 -3 4 1 -3 -5 -8

29. Ex 4: Identify the answer as positive, negative or zero. DO NOT SOLVE.–
negative
-0.8 – 0.8
-5 - 𝟑 𝟑 𝟒
−𝟑 𝟏 𝟐 – (−𝟑 𝟏 𝟐 )
𝟏 𝟐 −(− 𝟏 𝟒 )
−2.6 – (–3.6)
5.6 – 6.7
negative
zero
positive
positive
negative