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 =

Multiplication- is repeated addition!

“Three times four” or “Three groups of four”

+ + =

+4 +4 4= 12 square units3(4)=

Multiplication Repeated Addition

• You are going to get a handout (blue) called Multiply Integers Study Guide.

• You may use this as a study guide. • Take out something to write with.• Watch this slide show and follow along. • I will have you do problems on your

handout that go with problems on this slideshow.

• Do not work ahead.• I do not want you making any mistakes.

THE 1st NUMBER TELLS YOU:HOW MANY GROUPS YOU HAVE

If the 1st number is positive you are adding groups

If the 2nd 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 2nd NUMBER TELLS YOU: HOW MANY NUMBERS ARE IN EACH GROUP

If the 2nd number is negative your numbers in each group are negative.

Example #13(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.

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.

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!

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!

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

_ _ _ _ _ _ _ _ _

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!

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

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!

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!

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!

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!

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

Multiply

Integers

Objective - To multiply integers.

Signs arethe same

Signs aredifferent

Simplify.

1) 2 3

2) 4 8

3) 6(4)

4) 7( 8)

5) 2 5

6) 3( 10)

6

32

24

56

10

30

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!

– • + = –

Try These!

Simplify the following.

1) -6(7) =

2) 6(-7) =

3) 6 - 7 =

4) -6 - 7 =

-42

-42

-1

-13

Multiplying Multiple Integers

3( 4)( 5) 4( 3)( 2)

Another way...

Odd # of Negatives = Negative

Even # of Negatives = Positive

12 560

12 224

Aren’t integersinteresting?

TAKE OUT YOUR STUDY GUIDE

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!

– • + = –

+ + = +

– – = +

+ – = –

– + = –

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

Name___________September 3, 2009 Period___

Pg. 28 #1-15 All Write all problems down for full credit!