MULTIPLYING AND DIVIDING
INTEGERS
INTEGER PATTERNS
Column A
Column B
Column C
Column D
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
INTEGER MULTIPLICATION AND DIVISION
Column A
1.
In column A, what is the
sign of the numbers
being multiplied or
divided?
2.
In column A, what is the
sign of the answer?
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
INTEGER MULTIPLICATION AND DIVISION
Column D
1.
In column D, what is the
sign of the numbers
being multiplied or
divided?
2.
In column D, what is the
sign of the answer?
(-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
INTEGER MULTIPLICATION AND DIVISION
Column B
1.
In column B, what are
the signs of the
numbers being
multiplied or divided?
2.
In column B, what is the
sign of the answer?
-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
INTEGER MULTIPLICATION AND DIVISION
Column C
1.
In column C, what are
the signs of the
numbers being
multiplied or divided?
2.
In column C, what is the
sign of the answer?
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
INTEGER MULTIPLICATION AND DIVISION
Column A
4 · 2 = 8
3 · 1 = 3
1.
What is the
difference between
columns A and D?
Column D
(-4) · (-2) = 8
(-3) · (-1) = 3
5 · 8 = 40
(-5) · (-8) = 40
8 · 3 = 24
(-8) · (-3) = 24
6 · 6 = 36
(-6) · (-6) = 36
4 · 7 = 28
(-4) · (-7) = 28
8 ÷ 4 = 2
(-8) ÷ (-4) = 2
3 ÷ 3 = 1
(-3) ÷ (-3) = 1
40 ÷ 8 = 5
(-40) ÷ (-8) = 5
24 ÷ 3 = 8
(-24) ÷ (-3) = 8
36 ÷ 6 = 6
(-36) ÷ (-6) = 6
28 ÷ 7 = 4
(-28) ÷ (-7) = 4
INTEGER MULTIPLICATION AND DIVISION
Column B
-4 · 2 = -8
-3 · 1 = -3
1.
What is the
difference between
columns B and c?
Column C
4 · (-2) = -8
3 · (-1) = -3
-5 · 8 = -40
5 · (-8) = -40
-8 · 3 = -24
8 · (-3) = -24
-6 · 6 = -36
6 · (-6) = -36
-4 · 7 = -28
4 · (-7) = -28
-8 ÷ 4 = -2
8 ÷ (-4) = -2
-3 ÷ 3 = -1
3 ÷ (-3) = -1
-40 ÷ 8 = -5
40 ÷ (-8) = -5
-24 ÷ 3 = -8
24 ÷ (-3) = -8
-36 ÷ 6 = -6
36 ÷ (-6) = -6
-28 ÷ 7 = -4
28 ÷ (-7) = -4
1.
What rules for can you derive for
multiplying and dividing integers?
2.
Take 2 minutes and discuss everything you
understand so far about multiplying and
dividing integers.
MULTIPLYING AND DIVIDING INTEGERS
TO MULTIPLY OR DIVIDE INTEGERS, FOLLOW THESE STEPS:
1.
2.
3.
Multiply and divide as NORMAL.
How many negatives are in the problem?
An odd number of negatives = negative
An even number of negatives = positive
MULTIPLYING OR DIVIDING
INTEGERS
4.
How many negatives?
Is this even or odd?
My answer will be:
EXAMPLES
1.
-4 · 2 = ?
How many negatives?
Is this even or odd?
My answer will be:
2.
3.
5.
6.
-25 ÷ -5 = ?
How many negatives?
Is this even or odd?
My answer will be:
10 · (-3) = ?
How many negatives?
Is this even or odd?
My answer will be:
16 ÷ -4 = ?
How many negatives?
Is this even or odd?
My answer will be:
-3 · (-2) = ?
How many negatives?
Is this even or odd?
My answer will be:
(-1)(-2)(-3) = ?
7.
-20 ÷ -5 ÷ -4 = ?
How many negatives?
Is this even or odd?
My answer will be:
HELPFUL HINTS TO REMEMBERING YOUR SIGNS!
MULTIPLYING AND DIVIDING ONLY!!
Integer Tic-Tac-Toe
Integer Triangle
When multiplying or dividing 2 numbers:
When multiplying or dividing 2 numbers:
Cover the two signs on the triangle that are
in your problem.
Cover the two signs on any row, column,
or diagonal.
The sign remaining is the sign that your
answer will be.
The sign remaining is the sign that your
answer will be.
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-
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