1. For each value, write it opposite, then its absolute value.
p.6 - Integer Arithmetic
For each value, write it opposite, then its absolute value.
Watch this:
opposite absolute value

2. –7 ABSOLUTE VALUE 1. |17| 2. |–29| 3. –|45| 4. –|–247| – 45 – 247 17
|17|
|–29|
–|45|
–|–247|
– 45
– 247 17 29
–45
–247
5. –| |
6. –|41 – 19|
*7. –| – 2 – 1|
8. –| –(–7)|
–| |
–| |
–| – 3 |
–| | –
– 22 – –7
–101
–22 –3

3. Integer Addition - With Counters
–3 + 9
Draw 3 negative counters ...
.. then 9 positive counters
Cancel opposites. +6
What’s left?
2 + –7
Draw 2 positive counters ...
. then 7 negative counters
Cancel opposites. –5
What’s left?
–6 + –4
Draw 6 negative counters ...
. then 4 negative counters
No opposites, so ... .
–10
What’s left?

4. . .

5. Integer Addition - Number Line.
–3 + 9 –7
–6 + –4
Start at 0
Start at 0
Start at 0
The first integer, -3, is the first move.
The first integer, 2, is the first move.
The first integer, -6, is the first move.
The second integer, 9, is the second move.
The second integer,–7, is the second move.
The second integer,–4, is the second move.
Where did you end up?
Where did you end up?
Where did you end up?
= 6
2 + –7 = -5
= -10 .
-6 + –4

6. .

7. Integer Addition - The Rules
–3 + 9 6
B –7
– 5
–6 + –4
– 10
Signs SAME or DIFFERENT?
 SAME ? ADD the absolute values
 DIFFERENT ? SUBTRACT the absolute values
Steal the sign of the bigger absolute value.
 That is the sign of your answer. 9 – 3
--- 6 + 7 – 2
--- 5 – 6 + 4
--- 10 – .

8. .

9. UPDATED - Integer Addition - Practice
–16 –6
–12 –2 4 4 –6 –2 –8 –1
–10 –5 1 –7
–10 5 –8 –4 –2 –9 5
–11 –7
–17 –6
–16
–10 –3 –3 –2 –2

10. Integer Addition - Practice
= – = – = – = – = –28
= = = – = = –8
= – = = – = = –31
= – = = =– = 41 .

11. –3 –13 Integer Subtraction - Using Counters +3 or 3 –4 – (–7) 11 – 14
For high school and college level math, it’s easier to think of
subtraction as adding the opposite .
I want to take away 14 positives!
I want to take away 5 positives!
I want to take away 7 negatives!
SUBTRACTION – 14 –8 – 5 –4 – (–7)
is the same as or or or
ADDING THE OPPOSITE
(–14)
–8 + (–5)
–4 + (+7)
–4 – (–7)
11 – 14
–8 – 5 or or or
–4 + (+7)
(–14)
–8 + (–5) or
–4 + 7 –3
–13
+3 or 3 .

12. .

13. –8 – 5 = –13 = +3 –4 – (–7) Integer Subtraction - Using Number Line.
– 14
–8 – 5
–4 – (–7)
Start at 0.
Start at 0.
Start at 0.
The first integer, +11, is the first move.
The first integer, –8, is the first move (left).
The first integer, –4, is the first move.
The subtraction sign
means to move to the left...
The subtraction sign
also means to move to the left...
The subtraction sign
means move to the left...
... but the negative sign reverses it, so...
...the second integer, +14, means
move 14 to the left.
...the second integer, +5, means move 5 spaces to the left.
...move to the right 7 spaces.
Where did you end up?
Where did you end up?
Where did you end up?
11 – 14 = -3
–8 – 5 = –13
= +3 .
–4 – (–7)

14. .

15. Integer Subtraction - The Rules
11 – 14 11 3
–8 ─ 5 ─8
–4 ─ (–7)
–4 + (+7)
KEEP  CHANGE  CHANGE
the subtraction the sign
first to of the
value addition nd value
2. Signs SAME or DIFFERENT?
 SAME ? ADD the absolute values
 DIFFERENT ? SUBTRACT the absolute values
3. Steal the sign of the bigger absolute value.
 That is the sign of your answer. +
(─14) 14 – 11
--- 3 – 8 + 5
--- 13 +
(─5) – – 13 7 - 4
--- 3 . +

16. Integer Subtraction - The Rules
11 – 14
a. CHANGE the subtraction to addition, then...
b. CHANGE the sign of the 2nd integer [ “– 14” --> “+ (–14)” ]
c. IGNORE the original problem.
2. What’s the sign on the bigger absolute value?
** NEGATIVE (–14) so the answer is NEGATIVE**
Now, signs are DIFFERENT, SUBTRACT the absolute values.
4. Write down that number.
b. CHANGE the sign of the 2nd integer [ “– 5” --> “+ (–5)” ]
** NEGATIVE (–8) so the answer is NEGATIVE**
Now, signs are SAME, so ADD the absolute values.
b. CHANGE the sign of the 2nd integer [ “– (–7)” --> “+ (+7)” --> +7 ]
** POSITIVE (+7) so the answer is POSITIVE **
11 + –14 14 – 11
--- 3 –3
– 8 – 5
– 8 + –5 8 + 5
--- 13
–13
– 4 – (–7) 7 – 4
--- 3 – +3 .

17. Integer Subtraction - Practice
= – = – = – = – = –59
= – = – = = = –37
= = = = = 36 1. 2. 3. 4. 5. 6. 7. 8. 9.
10.
11.
12.
13.
14.
15.
– 16 – ( – 95)
– 5 – ( – 9) .

18. UPDATED - Integer Subtraction - Practice11 13 1 5 17 3 –1 2 –8 4 2 –2 –5 –2 –4 3 –8 13
–11 12 13 –1 6 3 3 . –1 4 –2 –1

19. –4 Integer Multiplication - Using Counters
–4 • 5
Draw 4 negative counters ...
... 5 TIMES
–4 • 5 = –20
Integer Division - Using Counters
–28 7
Draw 28 negative counters ...
... then DIVIDE them into 7 groups –4
–28 7 = .

20. .

21. –18 –14 Integer Multiplication - Using Number Line
Draw a dot at zero
1. –6 • 3
The 1st integer, –6 , tells you the size of the jump.
–18
The 2nd integer, 3 , tells you how many TIMES.
So, jump 6 backward 3 TIMES.
Integer Division - Using Number Line
Draw a dot at zero
–42 3
The 1st integer, –42 , is the total
The 2nd integer, 3 , tells you into how many pieces to DIVIDE it.
–14
So, DIVIDE the –42 into 3 pieces. .
How big is each piece?

22. .

23. – 56 10 + 2. Integer Multiplication - The Rules 1. –7 • 8
1. –7 • 8
When you multiply or divide integers, it’s easy:
Look at the signs:
If they’re the SAME ...
then, the answer’s POSITIVE
Signs are different, so the answer is negative. – 56
If they’re DIFFERENT
then, the answer’s NEGATIVE
Multiply the absolute values.
Integer Division - The Rules
When you multiply or divide integers, it’s easy:
–90 –9 2.
Look at the signs:
If they’re the SAME ...
Signs are the same , so the answer is positive.
then, the answer’s POSITIVE
If they’re DIFFERENT
then, the answer’s NEGATIVE + 10 .
Divide the absolute values.

24. .

25. Integer Multiplication and Division - Practice1. 2. 3. 4.
= – = – = 143
= = – = – 24
= – = = – 96
= = =– 200
= – = – = 17
= – = – = 13 5. 6. 7. 8. 9.
10.
11.
12.
13.
14.
15.
16.
17.
18. .

26. Integer Multiplication and Division - Practice36 36 36 36 –6 –6 –6 –6
– 4
– 4
– 4
– 4
–32
–32
–32
–32
– 7
– 7
– 7
– 7 16 16 16 16 6 6 6 6 72 . 72 72 72

27. Integers Operations . 4
-10 1 7
-50 -1
-125 -5 4 3 -8 -3 -1 1 -3 -9 -7 96 -4 -3 .

28. .

29. So, to simplify an expression using order of operations, you should:
Order of Operations, p. 2
Simplify 3(4 - 2) - 8 ÷ 3
(4 - 2)
- 8 ÷
1. First, simplify inside parenthesis 3
(2)
- 8 22
+ 9
2. Next, evaluate the exponent. ÷ 3
(2) 8 - 4
+ 9
3. Then, multiply or divide. ÷
* Which one first? 6 ─ 2
+ 9
Always work from left to right. 4
+ 9
4. Finally, add or subtract. 13
Always work from left to right.
So, to simplify an expression using order of operations, you should:
Multiply or
Divide
Add or
Subtract
Simplify Parenthesis
Evaluate Exponents
Order of Operations, p. 2

30. –1 Order of Operations –10 10 –1 –61 –32 51 =
11 – 32 ÷ 8 • – 7 + (– 9)(12) ÷ 2
(–6) ÷ 3 – (–12)(–4) 4. [48 – (12 – 14) • 2] + 8 ÷ (–8)
5. – – (–8 + 2)
(–5 + 9)3 + (–2)
11 – • 3
– 7 + (–108) ÷ 2
11 –
– (–54) –1
–61
(–2) – (–12)(–4)
[48 – (–2) • 2] + 8 ÷ (–8)
(–2) –
[48 – (–4) ] + 8 ÷ (–8)
÷ (–8) –
(–1)
–32 51
– – (–8 + 2)
–10 –1
– – (–6) =
( )3 + (–2)
–16 – (–6) 10 .
12 + (–2)
denominator (bottom) = 10
numerator (top) = –10

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