1. M ULTIPLYING AND D IVIDING I NTEGERS

2. I NTEGER P ATTERNS Column AColumn BColumn CColumn D 4 · 2 = 8-4 · 2 = -84 · (-2) = -8(-4) · (-2) = 8 3 · 1 = 3-3 · 1 = -33 · (-1) = -3(-3) · (-1) = 3 5 · 8 = 40-5 · 8 = -405 · (-8) = -40(-5) · (-8) = 40 8 · 3 = 24-8 · 3 = -248 · (-3) = -24(-8) · (-3) = 24 6 · 6 = 36-6 · 6 = -366 · (-6) = -36(-6) · (-6) = 36 4 · 7 = 28-4 · 7 = -284 · (-7) = -28(-4) · (-7) = 28 8 ÷ 4 = 2-8 ÷ 4 = -28 ÷ (-4) = -2(-8) ÷ (-4) = 2 3 ÷ 3 = 1-3 ÷ 3 = -13 ÷ (-3) = -1(-3) ÷ (-3) = 1 40 ÷ 8 = 5-40 ÷ 8 = -540 ÷ (-8) = -5(-40) ÷ (-8) = 5 24 ÷ 3 = 8-24 ÷ 3 = -824 ÷ (-3) = -8(-24) ÷ (-3) = 8 36 ÷ 6 = 6-36 ÷ 6 = -636 ÷ (-6) = -6(-36) ÷ (-6) = 6 28 ÷ 7 = 4-28 ÷ 7 = -428 ÷ (-7) = -4(-28) ÷ (-7) = 4

3. I NTEGER 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 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. I NTEGER 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

5. I NTEGER 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

6. I NTEGER 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 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

7. I NTEGER MULTIPLICATION AND DIVISION 1. What is the difference between columns A and D? 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

8. I NTEGER 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 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

9. 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.

10. M ULTIPLYING AND D IVIDING I NTEGERS T O 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

11. M ULTIPLYING OR D IVIDING I NTEGERS E XAMPLES 1. -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:

12. H ELPFUL H INTS 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. + - -