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. + - - + - - - + - - - +