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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:

2. 4). ? 28
Check:
( 7 )(4) = 28 = ? 4
Divide into 4 pieces. 28 7 7 7 7 7 7 7 7 7
= 28

3. 5). ? 45
Check:
( 9 )(5) = 45 = ? 5
Divide into 5 pieces. 45 9 9 9 9 9 9 9 9 9 9 9
= 45

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

5. -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

6. 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

7. 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

8. - 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

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

10. 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

11. 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

12. 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

13. 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.

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

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