The document provides instruction on multiplying integers. It explains that multiplication is repeated addition and presents rules for determining the sign of the product when multiplying integers. Examples are worked through step-by-step using models to represent multiplication as groups of numbers. Practice problems are provided for students to simplify expressions involving integer multiplication.

1. 1) - 3 - - 10 = 2) + 6 - - 9 = 3) - 4 + - 7 = 4) + 6 - 8 = 5) - 3 - - 12 = 6) - 7 - 12 = 7) + 5 - - 18 = 8) - 14 - - 6 = 9) + 7 - - 5 = 10) - 7 + - 8 = 11) - 6 - - 4 = 12) - 5 + 16 = 13) - 17 - - 12 = 14) + 13 - - 4 = Warm Up #10: Integer Review

2. Multiply Integers

3. Understanding Multiplication Multiplication - is repeated addition! “ Three times four” or “ Three groups of four” + + = + 4 + 4 4 = 12 square units 3(4) =

5. Directions For Using a Model to Multiply Integers THE 1 st NUMBER TELLS YOU: HOW MANY GROUPS YOU HAVE If the 1st number is positive you are adding groups If the 2 nd number is positive your numbers in each group are positive . If the 1st number is negative you are taking away groups . If you take away something you need a zero bank. THE 2 nd NUMBER TELLS YOU: HOW MANY NUMBERS ARE IN EACH GROUP If the 2 nd number is negative your numbers in each group are negative.

6. Example #1 3(6) = Add 3 groups of positive 6 Example #2 -6(5) = Take away 6 groups of positive 5. Example #3 -2(-6) = Take away 2 groups of negative 6.

7. Write out what each multiplication problem means. 1) -5(2) = Take away 5 groups of +2. You do NOT need to solve these! 2) 3(-2) = Add 3 groups of -2 . 3) -5(-4) = Take away 5 groups of -4 . 4) -8(1) = Take away 8 groups of +1.

8. Write out what each multiplication problem means. 5) -2(-4) = Take away 2 groups of -4 . 6) 11(3) = Add 11 groups of +3. 7) 7(-3) = Add 7 groups of -3 . 8) -8(6) = Take away 8 groups of +6. Turn your paper over!

9. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. 1) -3(2) = Take away 3 groups of +2 + + + + + + _ _ _ _ _ _ = -6 Start with 6 zeros first!

10. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. 2) 5(-3) = Add 5 groups of -3 _ _ _ _ _ _ = -15 _ _ _ _ _ _ _ _ _

11. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. 3) -2(-4) = Take away 2 groups of -4 + + + + + + + + _ _ _ _ _ _ _ _ = +8 Start with 8 zeros first!

12. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. 4) 1(-4) = Add 1 group of -4 _ _ _ _ = -4

13. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. 5) -4(2) = Take away 4 groups of +2 + + + + + + + + _ _ _ _ _ _ _ _ = -8 Start with 8 zeros first!

14. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. Try # 6 & 7 on your own!

15. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. 6) -1(3) = Take away 1 group of +3 + + + _ _ _ = -3 Start with 3 zeros first!

16. Draw a picture to solve each problem. If you are taking something away start with a zero bank. To show that you take it away, circle it and attach an arrow to it. Write the final value or answer. 7) -3(4) = Take away 3 groups of +4 + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ = -12 Start with 12 zeros first!

17. After doing these problems, try to write you own set of rules that describes how to multiply INTEGERS without using a model. Look at the examples on your paper to see a pattern. 8) A positive times a positive is a POSITIVE 2(6) = 12 9) A negative times a negative is a POSITIVE -2 ( -4 ) = 8 10) A negative times a positive is a NEGATIVE -1 (3) = -3 11) A positive times a negative is a NEGATIVE 1( -4 ) = -4 12) When the signs are the same and you multiply the answer is POSITIVE 3(4) = +12 -3 ( -4 )= +12 13) When the signs are the different & you multiply the answer is NEGATIVE -3 (4) = -12 3 ( -4 )= -12

18. Multiply Integers

19. Objective - To multiply integers. Signs are the same Signs are different Simplify. 1) 2) 3) 4) 5) 6)

20. An Easy Way To Remember How To Multiply Integers When good things, happen to good people, that’s good! + • + = + When bad things, happen to bad people, that’s good! – • – = + When good things, happen to bad people, that’s bad! + • – = – When bad things, happen to good people, that’s bad! – • + = –

21. Try These! Simplify the following. 1) -6(7) = 2) 6(-7) = 3) 6 - 7 = 4) -6 - 7 = -42 -42 -1 -13

22. Multiplying Multiple Integers Another way... Odd # of Negatives = Negative Even # of Negatives = Positive

23. Aren’t integers interesting? TAKE OUT YOUR STUDY GUIDE

24. To Remember Multiply & Divide Integers #20 When good things, happen to good people, that’s good! + • + = + When bad things, happen to bad people, that’s good! – • – = + When good things, happen to bad people, that’s bad! + • – = – When bad things, happen to good people, that’s bad! – • + = – +  + = + –  – = + +  – = – –  + = –

25. RULES FOR DIVIDING INTEGERS When determining the sign, the rules of multiplying integers are the same for dividing integers. If the signs are the same , the answer is positive . - 64  - 8 = 8 If the signs are different , the answer is negative . - 8  4 = -2 #21

26. Name___________ September 3, 2009 Period___ Pg. 28 #1-15 All Write all problems down for full credit!