1. Multiplying and Dividing Integers

2. Integer Patterns Column A Column B Column C Column D 4 · 2 = 8
4 · 2 = 8
-4 · 2 = -8
4 · (-2) = -8
(-4) · (-2) = 8
3 · 1 = 3
-3 · 1 = -3
3 · (-1) = -3
(-3) · (-1) = 3
5 · 8 = 40
-5 · 8 = -40
5 · (-8) = -40
(-5) · (-8) = 40
8 · 3 = 24
-8 · 3 = -24
8 · (-3) = -24
(-8) · (-3) = 24
6 · 6 = 36
-6 · 6 = -36
6 · (-6) = -36
(-6) · (-6) = 36
4 · 7 = 28
-4 · 7 = -28
4 · (-7) = -28
(-4) · (-7) = 28
8 ÷ 4 = 2
-8 ÷ 4 = -2
8 ÷ (-4) = -2
(-8) ÷ (-4) = 2
3 ÷ 3 = 1
-3 ÷ 3 = -1
3 ÷ (-3) = -1
(-3) ÷ (-3) = 1
40 ÷ 8 = 5
-40 ÷ 8 = -5
40 ÷ (-8) = -5
(-40) ÷ (-8) = 5
24 ÷ 3 = 8
-24 ÷ 3 = -8
24 ÷ (-3) = -8
(-24) ÷ (-3) = 8
36 ÷ 6 = 6
-36 ÷ 6 = -6
36 ÷ (-6) = -6
(-36) ÷ (-6) = 6
28 ÷ 7 = 4
-28 ÷ 7 = -4
28 ÷ (-7) = -4
(-28) ÷ (-7) = 4

3. Integer multiplication and division
Column A
4 · 2 = 8
3 · 1 = 3
5 · 8 = 40
8 · 3 = 24
6 · 6 = 36
4 · 7 = 28
8 ÷ 4 = 2
3 ÷ 3 = 1
40 ÷ 8 = 5
24 ÷ 3 = 8
36 ÷ 6 = 6
28 ÷ 7 = 4
In column A, what is the sign of the numbers being multiplied or divided?
In column A, what is the sign of the answer?

4. Integer multiplication and division
Column D
(-4) · (-2) = 8
(-3) · (-1) = 3
(-5) · (-8) = 40
(-8) · (-3) = 24
(-6) · (-6) = 36
(-4) · (-7) = 28
(-8) ÷ (-4) = 2
(-3) ÷ (-3) = 1
(-40) ÷ (-8) = 5
(-24) ÷ (-3) = 8
(-36) ÷ (-6) = 6
(-28) ÷ (-7) = 4
In column D, what is the sign of the numbers being multiplied or divided?
In column D, what is the sign of the answer?

5. Integer multiplication and division
Column B
-4 · 2 = -8
-3 · 1 = -3
-5 · 8 = -40
-8 · 3 = -24
-6 · 6 = -36
-4 · 7 = -28
-8 ÷ 4 = -2
-3 ÷ 3 = -1
-40 ÷ 8 = -5
-24 ÷ 3 = -8
-36 ÷ 6 = -6
-28 ÷ 7 = -4
In column B, what are the signs of the numbers being multiplied or divided?
In column B, what is the sign of the answer?

6. Integer multiplication and division
Column C
4 · (-2) = -8
3 · (-1) = -3
5 · (-8) = -40
8 · (-3) = -24
6 · (-6) = -36
4 · (-7) = -28
8 ÷ (-4) = -2
3 ÷ (-3) = -1
40 ÷ (-8) = -5
24 ÷ (-3) = -8
36 ÷ (-6) = -6
28 ÷ (-7) = -4
In column C, what are the signs of the numbers being multiplied or divided?
In column C, what is the sign of the answer?

7. Integer multiplication and division
Column A
4 · 2 = 8
3 · 1 = 3
5 · 8 = 40
8 · 3 = 24
6 · 6 = 36
4 · 7 = 28
8 ÷ 4 = 2
3 ÷ 3 = 1
40 ÷ 8 = 5
24 ÷ 3 = 8
36 ÷ 6 = 6
28 ÷ 7 = 4
Column D
(-4) · (-2) = 8
(-3) · (-1) = 3
(-5) · (-8) = 40
(-8) · (-3) = 24
(-6) · (-6) = 36
(-4) · (-7) = 28
(-8) ÷ (-4) = 2
(-3) ÷ (-3) = 1
(-40) ÷ (-8) = 5
(-24) ÷ (-3) = 8
(-36) ÷ (-6) = 6
(-28) ÷ (-7) = 4
What is the difference between columns A and D?

8. Integer multiplication and division
Column B
-4 · 2 = -8
-3 · 1 = -3
-5 · 8 = -40
-8 · 3 = -24
-6 · 6 = -36
-4 · 7 = -28
-8 ÷ 4 = -2
-3 ÷ 3 = -1
-40 ÷ 8 = -5
-24 ÷ 3 = -8
-36 ÷ 6 = -6
-28 ÷ 7 = -4
Column C
4 · (-2) = -8
3 · (-1) = -3
5 · (-8) = -40
8 · (-3) = -24
6 · (-6) = -36
4 · (-7) = -28
8 ÷ (-4) = -2
3 ÷ (-3) = -1
40 ÷ (-8) = -5
24 ÷ (-3) = -8
36 ÷ (-6) = -6
28 ÷ (-7) = -4
What is the difference between columns B and c?

9. What rules for can you derive for multiplying and dividing integers?
Take 2 minutes and discuss everything you understand so far about multiplying and dividing integers.

10. Multiplying and Dividing Integers To multiply or divide integers, follow these steps:
Multiply and divide as NORMAL.
How many negatives are in the problem?
An odd number of negatives = negative
An even number of negatives = positive

11. Multiplying or Dividing Integers Examples
(-1)(-2)(-3) = ?
How many negatives?
Is this even or odd?
My answer will be:
16 ÷ -4 = ?
-25 ÷ -5 = ?
-20 ÷ -5 ÷ -4 = ?
-4 · 2 = ?
How many negatives?
Is this even or odd?
My answer will be:
-3 · (-2) = ?
10 · (-3) = ?

12. When multiplying or dividing 2 numbers:
Helpful Hints to remembering your signs! MULTIPLYING AND DIVIDING ONLY!!
Integer Triangle
When multiplying or dividing 2 numbers:
Cover the two signs on the triangle that are in your problem.
The sign remaining is the sign that your answer will be.
Integer Tic-Tac-Toe
When multiplying or dividing 2 numbers:
Cover the two signs on any row, column, or diagonal.
The sign remaining is the sign that your answer will be. + + - - -