Download Chapter 9 Signed Numbers

Chapter 9
Signed
Numbers
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
9.3
Multiplying and Dividing
Signed Numbers
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplication with Different Signs
Notice the following pattern when multiplying
numbers with different signs.
This number
decreases by
1 each time.
3(4) =
2(4) =
12
8
1(4) =
0(4) =
–1(4) =
4
0
–4
–2(4) =
–3(4) =
–8
–12
This number
decreases by
4 each time.
The pattern suggests that when
we multiply a positive number
by a negative number, we get a
negative number.
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplication with Different Signs
Multiplication of Signed Numbers with Different Signs
To multiply two numbers with different signs, multiply the
absolute value. The result is negative.
Example:
Multiply. –6(4)
–6(4) = –24
Example:
Multiply. 12(–9)
The result will always be negative.
12(–9) = –108
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Division with Different Signs
Division of Signed Numbers with Different Signs
To divide two numbers with different signs, divide the
absolute value. The result is negative.
Example:
Divide. –36 ÷ 4
–36 ÷ 4 = – 9
Example:
Divide. 100 ÷ (–20)
The result will always be negative.
100 ÷ (–20) = –5
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplication with Same Signs
Notice the following pattern when multiplying two
negative numbers.
This number
decreases by
1 each time.
3(–4) = –12
2(–4) = –8
1(–4) = –4
0(–4) =
–1(–4) =
–2(–4) =
0
4
8
–3(–4) =
12
This number
increases by
4 each time.
The pattern suggests that
when we multiply two
negative numbers, we get a
positive number. (The same
is true for division of signed
numbers with the same sign.)
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplication with Same Signs
Multiplication and Division of Signed Numbers with the
Same Signs
To multiply or divide two numbers with the same sign,
multiply or divide the absolute values. The result is positive.
Example:
Divide. –75 ÷ (– 3)
–75 ÷ (– 3) = 25
Example:
2
Multiply.  5 
 

 12  3 
The result will always be positive.
1
 5  2   5
 12  3  18
 6  
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.
Multiplying Three or More Signed Numbers
Example:
Multiply. –8(–3)(2)
–8(–3)(2) = 24(2) First multiply –8(–3) = 24.
= 48
Then multiply 24(2) = 48.
Example:
2
2 3
Perform the operations.  3    3 
 5 
    
 2    2  3    2    3  3
 3   3  5   3   2  5  To divide the first two fractions,
         
invert and multiply the second
3

 1  
fraction.
 5
3
  
 5
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.