multiplication and division of real numbers chapter 1 section 8 mth 11203 algebra
TRANSCRIPT
MULTIPLICATION AND DIVISION OF REAL NUMBERS
CHAPTER 1 SECTION 8
MTH 11203Algebra
Multiply Numbers
The Sign of the Product of Two Real Numbers Rule 1 The product of two numbers with like signs is a
positive number(-) (-) = +
(+) (+) = +
Rule 2 The product of two numbers with unlike signs is a negative number
(+) (-) = -
(-) (+) = -
Multiplication and division of decimals are covered in appendix A
Multiply Numbers
Example 18 -4(2) = -8 neg because different signs
Example 20 6(-2) = -12 neg because different signs
Example 21 (-8)(-10) = 80 pos because same signs
Example (6)(-9) = -54 neg because different signs
Multiply Numbers
Example (-8)(-4) = 32 pos because same signs
Example (0)(-8) = 0 0 is never pos or neg
Example (-4)(-6) = 24 pos because same signs
Careful not to confuse subtraction with multiplication
Example -4 ndash 5 (-4)(-5)
-4 + (-5) 20
-9
Multiply Numbers
Example
Example
Remember that negatives can be written different ways
1 5 ( 1)( 5) 5
6 7 (6)(7) 42
1 3 (1)( 3) 3 1 1 or -
3 5 (3)(5) 15 5 5
or or - a a a
b b b
Multiply Numbers
Multiplication of more that one number in a given problem
Helpful hint Even number of negatives will equal a positive result Odd number of negatives will equal a negative result
Example 90 pg 67
4(-2)(-1)(-5) Odd negatives equals negative results
(-8)(-1)(-5)
(8)(-5)
-40
Multiply Numbers
Example
(-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results
(6)(-2)(-4)
(-12)(-4)
48Example
(-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results
(108)(-3)
-324
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Multiply Numbers
The Sign of the Product of Two Real Numbers Rule 1 The product of two numbers with like signs is a
positive number(-) (-) = +
(+) (+) = +
Rule 2 The product of two numbers with unlike signs is a negative number
(+) (-) = -
(-) (+) = -
Multiplication and division of decimals are covered in appendix A
Multiply Numbers
Example 18 -4(2) = -8 neg because different signs
Example 20 6(-2) = -12 neg because different signs
Example 21 (-8)(-10) = 80 pos because same signs
Example (6)(-9) = -54 neg because different signs
Multiply Numbers
Example (-8)(-4) = 32 pos because same signs
Example (0)(-8) = 0 0 is never pos or neg
Example (-4)(-6) = 24 pos because same signs
Careful not to confuse subtraction with multiplication
Example -4 ndash 5 (-4)(-5)
-4 + (-5) 20
-9
Multiply Numbers
Example
Example
Remember that negatives can be written different ways
1 5 ( 1)( 5) 5
6 7 (6)(7) 42
1 3 (1)( 3) 3 1 1 or -
3 5 (3)(5) 15 5 5
or or - a a a
b b b
Multiply Numbers
Multiplication of more that one number in a given problem
Helpful hint Even number of negatives will equal a positive result Odd number of negatives will equal a negative result
Example 90 pg 67
4(-2)(-1)(-5) Odd negatives equals negative results
(-8)(-1)(-5)
(8)(-5)
-40
Multiply Numbers
Example
(-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results
(6)(-2)(-4)
(-12)(-4)
48Example
(-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results
(108)(-3)
-324
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Multiply Numbers
Example 18 -4(2) = -8 neg because different signs
Example 20 6(-2) = -12 neg because different signs
Example 21 (-8)(-10) = 80 pos because same signs
Example (6)(-9) = -54 neg because different signs
Multiply Numbers
Example (-8)(-4) = 32 pos because same signs
Example (0)(-8) = 0 0 is never pos or neg
Example (-4)(-6) = 24 pos because same signs
Careful not to confuse subtraction with multiplication
Example -4 ndash 5 (-4)(-5)
-4 + (-5) 20
-9
Multiply Numbers
Example
Example
Remember that negatives can be written different ways
1 5 ( 1)( 5) 5
6 7 (6)(7) 42
1 3 (1)( 3) 3 1 1 or -
3 5 (3)(5) 15 5 5
or or - a a a
b b b
Multiply Numbers
Multiplication of more that one number in a given problem
Helpful hint Even number of negatives will equal a positive result Odd number of negatives will equal a negative result
Example 90 pg 67
4(-2)(-1)(-5) Odd negatives equals negative results
(-8)(-1)(-5)
(8)(-5)
-40
Multiply Numbers
Example
(-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results
(6)(-2)(-4)
(-12)(-4)
48Example
(-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results
(108)(-3)
-324
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Multiply Numbers
Example (-8)(-4) = 32 pos because same signs
Example (0)(-8) = 0 0 is never pos or neg
Example (-4)(-6) = 24 pos because same signs
Careful not to confuse subtraction with multiplication
Example -4 ndash 5 (-4)(-5)
-4 + (-5) 20
-9
Multiply Numbers
Example
Example
Remember that negatives can be written different ways
1 5 ( 1)( 5) 5
6 7 (6)(7) 42
1 3 (1)( 3) 3 1 1 or -
3 5 (3)(5) 15 5 5
or or - a a a
b b b
Multiply Numbers
Multiplication of more that one number in a given problem
Helpful hint Even number of negatives will equal a positive result Odd number of negatives will equal a negative result
Example 90 pg 67
4(-2)(-1)(-5) Odd negatives equals negative results
(-8)(-1)(-5)
(8)(-5)
-40
Multiply Numbers
Example
(-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results
(6)(-2)(-4)
(-12)(-4)
48Example
(-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results
(108)(-3)
-324
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Multiply Numbers
Example
Example
Remember that negatives can be written different ways
1 5 ( 1)( 5) 5
6 7 (6)(7) 42
1 3 (1)( 3) 3 1 1 or -
3 5 (3)(5) 15 5 5
or or - a a a
b b b
Multiply Numbers
Multiplication of more that one number in a given problem
Helpful hint Even number of negatives will equal a positive result Odd number of negatives will equal a negative result
Example 90 pg 67
4(-2)(-1)(-5) Odd negatives equals negative results
(-8)(-1)(-5)
(8)(-5)
-40
Multiply Numbers
Example
(-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results
(6)(-2)(-4)
(-12)(-4)
48Example
(-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results
(108)(-3)
-324
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Multiply Numbers
Multiplication of more that one number in a given problem
Helpful hint Even number of negatives will equal a positive result Odd number of negatives will equal a negative result
Example 90 pg 67
4(-2)(-1)(-5) Odd negatives equals negative results
(-8)(-1)(-5)
(8)(-5)
-40
Multiply Numbers
Example
(-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results
(6)(-2)(-4)
(-12)(-4)
48Example
(-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results
(108)(-3)
-324
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Multiply Numbers
Example
(-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results
(6)(-2)(-4)
(-12)(-4)
48Example
(-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results
(108)(-3)
-324
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Multiply Numbers
Example
(-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results
(8)(-3)(-5)
(-24)(-5)
120
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Divide Numbers
The Sign of the Quotient of Two Real Numbers Rule 1 The Quotient of two numbers with like signs
is a positive number(-) divide (-) = +
(+) divide (+) = +
Rule 2 The Quotient of two numbers with unlike signs is a negative number
(+) divide (-) = -
(-) divide (+) = -
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Divide Numbers
Example 52 pg 66 Example 50 pg 66
25 divide 5 or
Example 54 pg 66 Example 53 pg 66
18 22
9 1
30 55
6 1
25 55
5 1
36 44
9 1
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Divide Numbers
Example 50 pg 66
-1237 divide 32 or
387
places decimal two toround
865323
3712
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Divide Numbers
Example Example
Example
91
9
4
36
51
5
9
45
1571 decimals two toround
7051543
453
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Divide Numbers
Example 80 pg 66
Remember
We should write all fractions with the negative in front this will be the class standard
16 5 16 9 ( 16)( 9
3 9 3 5
3
)
( 31
( 16)(3) 48 3 or 9
(1)(5) 5 5)(5)
a a a
b b b
a
b
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Divide Numbers
Example
Example
7
4
7
4
1
2
7
2
2
1
7
2
2
7
2
7
2
7
1
1
8
35
5
4
35
8
5
4
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Summary of Operation of Real Numbers
Page 64 Summarizes of Operation of Real Numbers Addition Subtraction Multiplication Division
This is a good chart to use as a study guide for a test
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Evaluate Divisions Involving 0
Zero Divided by a Nonzero Number If a represents any real number except 0 then
Examples
00 0 0a a
a
62 because 3bull 2 6
3
00 because 1bull 0 0
1
0 (6)(0) because 06
0
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
Evaluate Divisions Involving 0
Division by Zero If a represents any real number except 0 then
Examples
0 is undefined0
aa
1undefined
0
0can not be determined no answer
0
numberget that andnumber aby 0 multiplecannot
undefined0
2
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95
HOMEWORK 18
Page 66 - 67
17 19 26 29 33 35 43 45 51 62 63 67 95