Beginning Algebra – 2

HFCC Math Lab

MULTIPLICATION AND DIVISION OF SIGNED NUMBERS PART I:

Multiplication of Signed Numbers Rules for Multiplication of Signed Numbers: (These Rules must be memorized.) Rule 1: To multiply two numbers with the same sign, multiply absolute values. The result is always positive. Rule 2: To multiply two numbers with different signs, multiply the absolute values. The result is always negative.

We can state the Multiplication Rules in another equivalent way:

Rule 1:

Rule 2:

Positive

Positive = Positive

Negative

Negative = Positive

Positive

Negative = Negative

Negative

Positive = Negative

Note: Even though 3 3 , the positive signs are included in some of the examples below for emphasis. Examples: (Rule 1)

1. ( 3) ( 5)

15 15

The signs are the same, so the answer is positive.

2. ( 6) ( 2)

12 12

The signs are the same, so the answer is positive.

3. ( 6) ( 1.1) 4. ( 6) ( 7)

6.6 6.6

The signs are the same, so the answer is positive.

42 42

5.

3 4

5 7

3 5 4 7

6.

1 2

4

1 4 2 1

The signs are the same, so the answer is positive. 15 28 4 2

15 28 2

The signs are the same, so the answer is positive.

The signs are the same, so the answer is positive.

Examples: (Rule 2) 1. ( 3) ( 4)

12

The signs are different, so the answer is negative.

2. ( 6) ( 4)

24

The signs are different, so the answer is negative.

3. ( 3) ( 1.2)

Revised 02/09

3.6

The signs are different, so the answer is negative.

1

4. ( 3) ( 0.7) 5. (6) ( 3)

2.1 18

6. ( 0.02) (0.4) 1 3

7.

8.

12

1 4

The signs are different, so the answer is negative.

3 5

The signs are different, so the answer is negative. 0.008

The signs are different, so the answer is negative.

1 12 3 1 13 4 5

12 3

4

3 20

The signs are different, so the answer is negative.

The signs are different, so the answer is negative.

When multiplying more than two signed numbers together do the multiplications one at a time from left to right. Examples: (Rules 1 and 2). Parentheses are used to indicate multiplication. 1. ( 2)( 3)( 5)

2. ( 3)( 2)( 7)

3. ( 2)( 4)( 1)

( 6)( 5)

( 6)( 7)

( 8)( 1)

30

42

8

4. ( 2)( 5)( 6)

5. ( 1)( 3)( 4)

( 10) ( 6)

3 ( 4)

60 7. (3)( 4)( 2)

6. (6)(2)( 1) (12)( 1)

12 8.

12

( 4) 2

9.

( 2)3

( 12)( 2)

( 4)( 4)

( 2)( 2)( 2)

24

16

( 4)( 2) 8

Note: In any multiplication problem: If there are an even number of negative factors, the answer is positive. See examples 1, 2 and 3 above. If there are an odd number of negative factors, the answer is negative. See examples 4, 5, 6 and 7 above.

Revised 02/09

2

PART II:

Division of Signed Numbers Rules for Division of Signed Numbers: (These Rules must be memorized.) Rule 1: To divide two numbers with the same sign, divide the absolute values. The result is always positive. Rule 2: To divide two numbers with different signs, divide the absolute values. The result is always negative.

We can state the Division Rules in another equivalent way:

Rule 1:

Positive

Positive = Positive

Negative

Negative = Positive

Positive

Negative = Negative

Negative

Positive = Negative

Rule 2:

Notice that the Rules for Division are the same as the Rules for Multiplication.

Examples: 1. ( 8) ( 4)

2

The signs are different, so the answer is negative.

2. ( 20) ( 5)

4

4

The signs are the same, so the answer is positive.

3. ( 40) ( 8)

5

The signs are different, so the answer is negative.

4. ( 50) ( 5)

10 10

The signs are the same, so the answer is positive.

5. ( 1.2) ( 0.3)

4

The signs are the same, so the answer is positive.

6. ( 2.8) ( 0.4)

7

4

The signs are different, so the answer is negative.

7. 18 ( 2)

9

The signs are different, so the answer is negative.

8. ( 24) 3

8

The signs are different, so the answer is negative.

Revised 02/09

3

Remember that a fraction bar means division. Therefore, we can simplify fractions containing signed numbers by using the Division Rules for signed numbers.

Examples: 1.

2 3

2 3

because a positive divided by a negative is negative.

2.

2 3

2 3

because a negative divided by a positive is negative.

3.

2 3

2 3

because a negative divided by a negative is positive.

4.

8 10

8 10

5.

12 18

12 18

6.

5 20

5 20

7.

4 3

5 2

4 3

8.

6 35

3 7

6 35

9.

1

1 3

1

8 2 10 2 12 6 18 6

2 3

5 5 20 5

4 5

Note: Be careful:

Revised 02/09

4 5

4 3

1 4 5 2

4 3

3 7

9 5

21 7 whereas 3

2 5

6 35

4 3

8 15 2

7 3

5 9

21 7

6 355 20 27

7

4

1

7 31

2 5

Exercises: Perform the following multiplications and divisions. 1. ( 3)( 6)

2. ( 2)( 2)( 2)( 2)

3. ( 3)( 4)

4. ( 2)(5)

5. (5)( 3)

6. ( 6)( 7)( 8)

7. ( 10) ( 5)

8.

9. ( 6) 2

10. ( 1) 6

11. ( 1) 7

12. ( 8)( 7)

13. ( 6) (2)

14. 8 ( 2)

15. ( 42) ( 6)

16. 16 ( 4)

3 4

17.

2 3

18.

19. ( 1.2) ( 0.4)

12 6

5 6

20. ( 1.5) 3

1 ( 7) 4

22.

2

23. ( 5)( 4)( 3)( 2)

24.

2 3

26.

2 3

21. 5

3 4

25.

5 7

5 8

1 3

4 5 7 5 6

Answers to all problems. Solutions to some problems. 1.

18

2. 16

3.

12

4.

10

5.

6.

336

7.

2

8. 2

10. 1

15

11.

9. ( 6) 2

1 Note: There are an odd number of negative factors, so the answer is negative.

12. 56

13.

3

15. 7

16.

4

17.

3 4

Revised 02/09

2 3

3 4

3 2

9 8

( 6)( 6) 36

1

1 8

5

14.

4

18.

25 42

Answers continued: 19. 3

20.

0.5

21. 5

1 ( 7) 4

21 ( 7) 4 21 7 4 1 3

22.

2

1 3

4

7 3

4 1

7 1 3 4

7 12

21 4

1 71

3 4

23. 120 Note: There are an even number of negative factors, so the answer is positive.

24.

2 3

5 7

2 3

25.

3 4

5 8

3 4

26.

2 3

5 6

5 7

2 5 3 7

5 8 2 3

3 5 4 8 5 6

10 21 15 32

2 3

6 5

2 31

2

6 5

4 5

NOTE: You can get additional instruction and practice by going to the following websites: http://www.themathpage.com/alg/multiply-divide-signed-numbers.htm This website gives rules for multiplying and dividing signed numbers along with many interactive examples. http://www.quia.com/jg/1669.html This website includes flashcards, matching and concentration games that can be used to practice the rules for multiplying and dividing signed numbers.

Revised 02/09

6