Discussion on addition of integers

2. All numbers are numbers. There are
two types of real numbers; they are
numbers and numbers. Natural
numbers, whole numbers, integers are all
numbers.
real
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 -3 + -2 = -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 -5 + 3
Remove all
the zero
pairs.
= -2

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

11. Add -6 + 5
Remove all
the zero
pairs.
= -1

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

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. Adding Integers with like signs.
- When the signs are the same, add the
numbers together and keep the sign.
-9 + -3 = -12
Adding integers with unlike signs.
- When the signs are different, subtract the
integers and keep the sign of the larger
integer.
-9 + 3 = -6

15. Let’s try a few examples using the rules for adding integers.
1) -8 + 8 =
2) -9 + -11 =
3) 13 + (-19) =
4) 7 + 5 =
5) -12 + 10 =
6) -22 + (-16) =
7) 18 + (-5) =
0
-20
-6
12
-2
-38
13

16. First and Last Name
November 29, 2017
Class Review
Simplify.
1.
−7
11
+
2
11
=
2.
−6
14
+
−4
14
=
−𝟕+𝟐
𝟏𝟏
=
−𝟓
𝟏𝟏
−𝟔+−𝟒
𝟏𝟒
=
−𝟏𝟎
𝟏𝟒
÷ 2
÷ 2
−𝟓
𝟕

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)
•-5 + 2 keep, change, change
•Opposite sign subtract and keep the
sign of the larger digit.
•-5 + 2 = -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. Example
6 – (-4)
6 + 4
Keep, Change, Change
10
Now follow the rules for
adding integers!

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

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

23. Time for some practice!
1. -9 – 5 =
2. 27 – (-8) =
3. -3 – (-1) =
4. -8 – 9 =
5. 14 – 17 =
6. 4 – (-19) =
-9 + -5 = -14
27 + 8 = 35
-3 + 1 = -2
-8 + -9 = -17
14 + -17 = -3
4 + 19 =23

24. Rewrite as an addition problem then solve.
1.5 – (-4) =
2.-7 – (-8) =
3.2 – 6 =
4.-12 – 12 =
5.-14 – (-14) =
5 + 4 = 9
-7 + 8 = 1
2 + -6 = -4
-12 + -12 = -24
-14 + 14 = 0

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

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

27. 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.
8 – 10 = 8 + -10 = – 2°F
Temp at 5:00 P.M.
Temp at 8:00 P.M.
– 2 – 5 = – 2 + -5 = – 7°F

28. Ex 3: Rewrite as an addition problem then solve.
To subtract an integer, add it’s opposite.
Keep, Change, Change
a) 6 – (-1) = + =
b) -4 – (-3) = + =
c) 1 – 6 = + =
d) -3 – (-4) = + =
e) -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.
a)-0.8 – 0.8
b)-5 - 𝟑
𝟑
𝟒
c)−𝟑
𝟏
𝟐
– (−𝟑
𝟏
𝟐
)
d)
𝟏
𝟐
−(−
𝟏
𝟒
)
e)−2.6 – (–3.6)
f) 5.6 – 6.7
– 0.8 + -0.8 negative
-5 + - 3
3
4 negative
- 3
1
2
+ 3
1
2 zero
1
2
+
1
4
positive
-2.6 + 3.6 positive
5.6 + -6.7 negative