MULTIPLYING AND DIVIDING INTEGERS

INTEGER PATTERNSColumn A Column B Column C Column D

4 · 2 = 8 -4 · 2 = -8 4 · (-2) = -8 (-4) · (-2) = 83 · 1 = 3 -3 · 1 = -3 3 · (-1) = -3 (-3) · (-1) = 35 · 8 = 40 -5 · 8 = -40 5 · (-8) = -40 (-5) · (-8) = 408 · 3 = 24 -8 · 3 = -24 8 · (-3) = -24 (-8) · (-3) = 246 · 6 = 36 -6 · 6 = -36 6 · (-6) = -36 (-6) · (-6) = 364 · 7 = 28 -4 · 7 = -28 4 · (-7) = -28 (-4) · (-7) = 288 ÷ 4 = 2 -8 ÷ 4 = -2 8 ÷ (-4) = -2 (-8) ÷ (-4) = 23 ÷ 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 DIVISIONColumn A

4 · 2 = 83 · 1 = 35 · 8 = 408 · 3 = 246 · 6 = 364 · 7 = 288 ÷ 4 = 23 ÷ 3 = 1

40 ÷ 8 = 524 ÷ 3 = 836 ÷ 6 = 628 ÷ 7 = 4

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?

INTEGER MULTIPLICATION AND DIVISION

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?

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

INTEGER MULTIPLICATION AND DIVISION

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?

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

INTEGER MULTIPLICATION AND DIVISION

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?

Column C4 · (-2) = -83 · (-1) = -3

5 · (-8) = -408 · (-3) = -246 · (-6) = -364 · (-7) = -288 ÷ (-4) = -23 ÷ (-3) = -140 ÷ (-8) = -524 ÷ (-3) = -836 ÷ (-6) = -628 ÷ (-7) = -4

INTEGER MULTIPLICATION AND DIVISION

1. What is the difference between columns A and D?

Column A4 · 2 = 83 · 1 = 35 · 8 = 408 · 3 = 246 · 6 = 364 · 7 = 288 ÷ 4 = 23 ÷ 3 = 140 ÷ 8 = 524 ÷ 3 = 836 ÷ 6 = 628 ÷ 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

INTEGER MULTIPLICATION AND DIVISION

1. What is the difference between columns B and c?

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 C4 · (-2) = -83 · (-1) = -3

5 · (-8) = -408 · (-3) = -246 · (-6) = -364 · (-7) = -288 ÷ (-4) = -23 ÷ (-3) = -140 ÷ (-8) = -524 ÷ (-3) = -836 ÷ (-6) = -628 ÷ (-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 INTEGERSTO MULTIPLY OR DIVIDE INTEGERS, FOLLOW THESE STEPS:

1. Multiply and divide as NORMAL.2. How many negatives are in the problem?3. An odd number of negatives = negative

An even number of negatives = positive

MULTIPLYING OR DIVIDING INTEGERS

EXAMPLES1. -4 · 2 = ?

How many negatives?Is this even or odd?My answer will be:

2. -3 · (-2) = ?How many negatives?Is this even or odd?My answer will be:

3. 10 · (-3) = ?How many negatives?Is this even or odd?My answer will be:

4. (-1)(-2)(-3) = ?How many negatives?Is this even or odd?My answer will be:

5. 16 ÷ -4 = ?How many negatives?Is this even or odd?My answer will be:

6. -25 ÷ -5 = ?How many negatives?Is this even or odd?My answer will be:

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!!

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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.

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