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- 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) =
- 4. <ul><li>You are going to get a handout ( blue ) called Multiply Integers Study Guide . </li></ul><ul><li>You may use this as a study guide. </li></ul><ul><li>Take out something to write with. </li></ul><ul><li>Watch this slide show and follow along. </li></ul><ul><li>I will have you do problems on your handout that go with problems on this slideshow. </li></ul><ul><li>Do not work ahead. </li></ul><ul><li>I do not want you making any mistakes. </li></ul>Multiply Integers
- 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!

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