Multiplying and Dividing Integers

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Presentation transcript:

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 (-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 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?

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?

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?

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?

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?

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?

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.

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

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) = ?

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. + + - - -