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Multiplying and Dividing Integers

2 3

-2 -3

-2 3

2 -3

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*If the two terms have the same sign the answer is

positive.

-15 x -2 = 30 -22 ÷ -11 = 2 12 x 6 = 72

* If the two terms have different

signs answer is negative.

-15 x 2 = -30 22 ÷ -11 = -2 -12 x 6 = -72

Multiplying and Dividing Integers

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The Party in MathlandHave you ever been to a party like this?

Everyone is happy and having a good time (they are ALL POSITIVE). Suddenly, who should appear but the GROUCH (ONE NEGATIVE)! The grouch goes around complaining to everyone about the food, the music, the room temperature, the other people....

What happens to the party? Everyone feels a lot less happy... the party may be doomed!! ONE NEGATIVE MAKES EVERYTHING NEGATIVE

But wait... is that another guest arriving?

What if another grouch (A SECOND NEGATIVE) appears? The two negative grouches pair up and gripe and moan to each other about what a horrible party it is and how miserable they are!! But look!! They are starting to smile; they're beginning to have a good time, themselves!!

PAIRS OF NEGATIVES BECOME POSITIVENow that the two grouches are together the rest of the people (who were really positive all along) become happy once again. The party is saved!!

The moral of the story is that (at least in math, when multiplying or dividing) the number of positives don't matter, but watch out for those negatives!!

To determine whether the outcome will be positive or negative, count the number of negatives: If there are an even number of negatives ­and you can put them in pairs­ the answer will be positive, if not... it'll be negative:

Negatives in PAIRS are POSITIVE; NOT in pairs, they're NEGATIVE.

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Positive Negative

Party in Mathland

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**___________ NUMBER OF NEGATIVES ~ ___________ ANSWER

**_____________ NUMBER OF NEGATIVES ~ _______________ ANSWER

a.) (-5)(-2)(-1)(-10) b.) (-2)(3)(-7)

a.) (-5)(-4)(-7) b.) (-12)(-1)(-5)(2)

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Examples

(-6)(2)(-3)

(3)(-1)(5)

(-4)(-2)(-10)

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PRACTICE

1. (5)(-13) 2. 12 (-4)

3. -72 ÷ (-8) 4. -81 ÷ 3

5. (-14)(-7) 6. 96 ÷ (-2)

7. (-4)(-13)(2) 8. (-8)(-6) ÷ (-3)

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~Exponents with Integers~

-42 (-4)2

~If negative sign _____________ parenthesis it is ______________in the base.

~If negative sign ______________ parenthesis it is ________________ in the base.

*Helpful Hint*

a.) (-2)3 b.) (-7)2 c.) -92

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~Solve the following~25

24

23

22

21

20

*Helpful Hint*

~Examples~

a.) 90 b.) (-12) 0 c.) 10

d.) -130 e.) 00

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http://www.mathwizz.com/integers/page5.htm

http://berghuis.co.nz/abiator/maths/sa/saintegermultiply.html

http://www.regentsprep.org/Regents/math/ALGEBRA/AOP3/Smixed.htm

http://www.regentsprep.org/Regents/math/ALGEBRA/AOP3/Sapp.htm

http://www.math­play.com/multiplying­and­dividing­integers­game.html

http://www.shodor.org/interactivate/activities/ArithmeticFour/?version=1.4.2_03&browser=MSIE&vendor=Sun_Microsystems_Inc.

http://www.quia.com/cb/64603.html

http://amby.com/educate/math/integ_x1.html

http://www.studyzone.org/mtestprep/math8/a/divintegersp.cfm

http://www.studyzone.org/mtestprep/math8/a/multintegersp.cfm

http://www.studyzone.org/mtestprep/math8/g/7dividngintegersq.cfm

http://www.studyzone.org/mtestprep/math8/g/7multiplyingsignedp.cfm

as a class

1st web site as center

2nd website for centers

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http://www.regentsprep.org/Regents/math/ALGEBRA/AOP3/Sapp.htm

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http://www.quia.com/cb/64603.html

http://www.shodor.org/interactivate/activities/ArithmeticFour/?version=1.4.2_03&browser=MSIE&vendor=Sun_Microsystems_Inc.

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http://www.quia.com/cb/64603.html

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http://www.quia.com/cb/64603.html

http://www.shodor.org/interactivate/activities/ArithmeticFour/?version=1.4.2_03&browser=MSIE&vendor=Sun_Microsystems_Inc.

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Integer Centers1. Integer Football (answer questions on worksheet)

2. Integer Problem Solving (show problem and answer on worksheet)

3. Quia integer jeopardy (winner gets sticker)http://www.quia.com/cb/64603.html

4. Regents prep website (write answers in notebook)http://www.regentsprep.org/Regents/math/ALGEBRA/AOP3/Smixed.htm

5. Integer Connect four (choose all four integer operations) http://www.shodor.org/interactivate/activities/ArithmeticFour/?version=1.4.2_03&browser=MSIE&vendor=Sun_Microsystems_Inc.

6. Regents prep word problems. (write answers in notebook)http://www.regentsprep.org/Regents/math/ALGEBRA/AOP3/Sapp.htm

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Add Subtract

Multiply/Divide Hints

1.

2.

1.

2.

1.

2.

1.

2.

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Name _____________________Date ______________

Integer Operations Practice Period ____________

**Directions** Complete the following problems inpencil and in your graph notebook. You must writethe problem and show the work in your notebookin order to receive full credit.

~Solve~

1. -83 + (-120) 2. 33 - 47 3. (-25)(-7)

4. 252 ÷ (-4) 5. 41 + (-19)6. (-220) ÷ (-11)

7. 33(-12) 8. -63 - (-88)9. 140 ÷ (-7) ÷(-5)

10. -24 - (-11) - 30 11. -27 + 62 + (-48)12. (-36)(-5)(-8)

~Solve the following word problems. You mustshow the problem and the work in your notebookin order to receive full credit.

13. A deep sea diver is at a depth of 9 feet below sealevel. The diver’s depth is changing by -5 feet per second. What is the diver’s position after 15 seconds?

14. A group of hikers on a mountain began at anelevation of 3,040 feet above sea level and stopped at anelevation of 2,319 feet below sea level. What was theirchange in elevation between these two points?

15. You record withdrawals and deposits in yourcheckbook. The starting balance was $65. The firsttransaction was a withdrawal for $72. The nexttransaction was a deposit of $37. Finally, you recorded awithdrawal of $42. How much money is your bankaccount after the three transactions?

16. The temperature at 6 A.M. was -5°F. At 3 P.M. the

temperature was 4 F. What was the change intemperature?

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*Exponents with negative signs*

-42 (-4)2~Apply odd and even # of factors to help determine the sign of the answer.

Helpful Hint

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