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Licensing information Users should treat this material as a working draft. This material can be used in its current form, customized, and/or printed or displayed by the user. The author(s) request feedback on all materials so that they can be continually improved and updated. This material is licensed under the Creative Commons Attribution-Share Alike license: (http://creativecommons.org/licenses/by-sa/3.0/). Author: Kevin Hall Wording for the legal statement above is adapted from the legal statement for Trigonometry, published in 2009 by The CK-12 Foundation: http://about.ck12.org/

4). ? 28 Check: ( 7 )(4) = 28 = ? 4 Divide into 4 pieces. 28 7 7 7 7 7 7 7 7 7 = 28

5). ? 45 Check: ( 9 )(5) = 45 = ? 5 Divide into 5 pieces. 45 9 9 9 9 9 9 9 9 9 9 9 = 45

Division and Multiplication Have the Same Rules • If the 2nd number is negative, you Flip the sign of the answer.

-10 -2 -5 -5 -10 Flip to Pos. 6). = ? Yes. Divide into 2 pieces. 5 5 Will answer be Pos or Neg? Flip to Pos. 6). -10 = ? -2 Will the sign flip? Yes. Divide into 2 pieces. 5 5 -5 “F” stands for “Flip” -5 -10

5 Stay Neg. 7). - 45 = ? No. Divide into 5 pieces. -9 -9 -9 -9 -9 -9 Will answer be Pos or Neg? Stay Neg. 7). - 45 = ? 5 Will the sign flip? No. Divide into 5 pieces. -9 -9 -9 -9 -9 -9 -45

Flip to Neg. 8). 45 = ? -5 Yes. Divide into 5 pieces. 45 9 9 9 9 9 -9 Will answer be Pos or Neg? Flip to Neg. 8). 45 = ? -5 Will the sign flip? Yes. Divide into 5 pieces. 45 9 9 9 “F” stands for “Flip” 9 9 -9 -9

- 5 Flip to Pos. 9). - 40 = ? Yes. Divide into 5 pieces. 8 8 -8 -8 -8 Will answer be Pos or Neg? Flip to Pos. 9). - 40 = ? - 5 Will the sign flip? Yes. Divide into 5 pieces. 8 8 -8 -8 -8 -8 -8 -40

Let’s show the picture for both dividing and checking Checking our answers: Let’s show the picture for both dividing and checking

Flip Flip -3 -6 -6 -6 10). 18 Check: ( -6 )(-3) = 18 = ? Yes. Divide into 3 pieces. 18 6 Flip Flip 6 = 18 6 6 6 6 Flip -6 -6 -6

Flip Flip -3 -6 -6 -6 WHY flip when dividing by a negative? 18 = ? 18 So why should we flip it, here, too? 18 6 We flip it here (multiplying). Check: ( -6 )(-3) = 18 Flip 6 = 18 6 6 6 6 Flip -6 -6 -6

Flip? -20 Why NOT flip when dividing by a positive? -20 Check: ( ? )(4) = -20 = ? 4 Do we flip it here? So why can’t we flip it here? No. Flip? We need to end up with -20 -20

Try Without a Picture -100 Stay Neg. Flip to Pos. a). b). 2 No. Yes. 11). Will answer be Pos or Neg? Stay Neg. Flip to Pos. Will answer be Pos or Neg? a). b). -100 -40 = 50 + or -50 ? = 4 or ? -4 2 -10 Will sign flip? Will sign flip? No. Yes.

Independent Practice Try these at your own pace. Don’t worry about finishing them all—just be accurate.

Flip to Pos. 12). - 15 16). - 15 - 3 3 Flip - 15 Flip to Neg. 3 13). = 5 + 2(4 – 6 ) - 3 3 Flip - 15 + 2( ) 4 + - 6 Flip to Neg. 3 13). 15 + 2( ) = - 3 - 5 - 2 - 3 Flip - 5 + - 4 14). 15 – - 3 - 9 15 + + 3 = 18 17). - 8 + ( ) - 8 + - 2 - 2 15). - 15 + - 3 = - 18 4 + - 10 - 6