multiplying and dividing monomials
DESCRIPTION
Multiplying and Dividing Monomials. Rules for Multiplication. When you multiply monomials and their bases are the same, you keep the base and add the exponents. Example: z 4 · z 2 = z 4+2 = z 6 Example: 5 2 · 5 9 = 5 2+9 = 5 11. Independent Practice. A. n 3 · n 2 B. f 6 · f 3 - PowerPoint PPT PresentationTRANSCRIPT
Multiplying Multiplying and Dividing and Dividing MonomialsMonomials
Rules for Rules for MultiplicationMultiplication When you multiply monomials When you multiply monomials
and their bases are the same and their bases are the same you keep the base and add the you keep the base and add the exponentsexponents
Example zExample z44 z z22 = z = z4+24+2 = z = z66
Example 5Example 522 5 599 = 5 = 52+92+9 = 5 = 51111
Independent Independent PracticePractice A nA n33 n n22
B fB f66 f f33
C 8 C 8 8 855
AnswersAnswers
AA nn55
BB ff99
CC 8866
Rules for DivisionRules for Division
When you divide monomials and When you divide monomials and their bases are the same you their bases are the same you keep the base and subtract the keep the base and subtract the exponentsexponents
Example bExample b1010 divide b divide b33 = b = b10-310-3 = b = b77
Example 6Example 655 divide 6 = 6 divide 6 = 65-15-1 = 6 = 644
Independent Independent PracticePractice
A wA w1212 divide w divide w55
B pB p66 divide p divide p44
C 9C 97 7 divide 9divide 922
AnswersAnswersAA ww77
BB pp22
CC 9955
Sample ARMT Sample ARMT QuestionsQuestions SimplifySimplify 661010 divide (6 divide (677 divide 6 divide 622)) Following the order of operations we would Following the order of operations we would
take care of the parenthesis first Since both take care of the parenthesis first Since both bases are 6 we keep the base and subtract bases are 6 we keep the base and subtract (because we are dividing) 7-2 = 5 Then we (because we are dividing) 7-2 = 5 Then we have 6have 61010 divided by 6 divided by 655 We have the same We have the same base so we keep it and subtract 10 - 5 = 5 base so we keep it and subtract 10 - 5 = 5 Our answer is 6Our answer is 655
Sample ARMT Questions Sample ARMT Questions ContCont
3355 3 388 3 322
3 3 3 333
Simplify the top simplify the bottom and then divideSimplify the top simplify the bottom and then divideSince the bases are the same throughout the whole Since the bases are the same throughout the whole
problem we know that the base of our answer will be 3 problem we know that the base of our answer will be 3 The top gives us 3The top gives us 35+8+25+8+2 = 3 = 31515
The bottom gives us 3The bottom gives us 31+31+3 = 3 = 344
Last we divide We keep the base of 3 and subtract the Last we divide We keep the base of 3 and subtract the exponents 15 ndash 4 = 11 Our answer is 3exponents 15 ndash 4 = 11 Our answer is 31111
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Rules for Rules for MultiplicationMultiplication When you multiply monomials When you multiply monomials
and their bases are the same and their bases are the same you keep the base and add the you keep the base and add the exponentsexponents
Example zExample z44 z z22 = z = z4+24+2 = z = z66
Example 5Example 522 5 599 = 5 = 52+92+9 = 5 = 51111
Independent Independent PracticePractice A nA n33 n n22
B fB f66 f f33
C 8 C 8 8 855
AnswersAnswers
AA nn55
BB ff99
CC 8866
Rules for DivisionRules for Division
When you divide monomials and When you divide monomials and their bases are the same you their bases are the same you keep the base and subtract the keep the base and subtract the exponentsexponents
Example bExample b1010 divide b divide b33 = b = b10-310-3 = b = b77
Example 6Example 655 divide 6 = 6 divide 6 = 65-15-1 = 6 = 644
Independent Independent PracticePractice
A wA w1212 divide w divide w55
B pB p66 divide p divide p44
C 9C 97 7 divide 9divide 922
AnswersAnswersAA ww77
BB pp22
CC 9955
Sample ARMT Sample ARMT QuestionsQuestions SimplifySimplify 661010 divide (6 divide (677 divide 6 divide 622)) Following the order of operations we would Following the order of operations we would
take care of the parenthesis first Since both take care of the parenthesis first Since both bases are 6 we keep the base and subtract bases are 6 we keep the base and subtract (because we are dividing) 7-2 = 5 Then we (because we are dividing) 7-2 = 5 Then we have 6have 61010 divided by 6 divided by 655 We have the same We have the same base so we keep it and subtract 10 - 5 = 5 base so we keep it and subtract 10 - 5 = 5 Our answer is 6Our answer is 655
Sample ARMT Questions Sample ARMT Questions ContCont
3355 3 388 3 322
3 3 3 333
Simplify the top simplify the bottom and then divideSimplify the top simplify the bottom and then divideSince the bases are the same throughout the whole Since the bases are the same throughout the whole
problem we know that the base of our answer will be 3 problem we know that the base of our answer will be 3 The top gives us 3The top gives us 35+8+25+8+2 = 3 = 31515
The bottom gives us 3The bottom gives us 31+31+3 = 3 = 344
Last we divide We keep the base of 3 and subtract the Last we divide We keep the base of 3 and subtract the exponents 15 ndash 4 = 11 Our answer is 3exponents 15 ndash 4 = 11 Our answer is 31111
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Independent Independent PracticePractice A nA n33 n n22
B fB f66 f f33
C 8 C 8 8 855
AnswersAnswers
AA nn55
BB ff99
CC 8866
Rules for DivisionRules for Division
When you divide monomials and When you divide monomials and their bases are the same you their bases are the same you keep the base and subtract the keep the base and subtract the exponentsexponents
Example bExample b1010 divide b divide b33 = b = b10-310-3 = b = b77
Example 6Example 655 divide 6 = 6 divide 6 = 65-15-1 = 6 = 644
Independent Independent PracticePractice
A wA w1212 divide w divide w55
B pB p66 divide p divide p44
C 9C 97 7 divide 9divide 922
AnswersAnswersAA ww77
BB pp22
CC 9955
Sample ARMT Sample ARMT QuestionsQuestions SimplifySimplify 661010 divide (6 divide (677 divide 6 divide 622)) Following the order of operations we would Following the order of operations we would
take care of the parenthesis first Since both take care of the parenthesis first Since both bases are 6 we keep the base and subtract bases are 6 we keep the base and subtract (because we are dividing) 7-2 = 5 Then we (because we are dividing) 7-2 = 5 Then we have 6have 61010 divided by 6 divided by 655 We have the same We have the same base so we keep it and subtract 10 - 5 = 5 base so we keep it and subtract 10 - 5 = 5 Our answer is 6Our answer is 655
Sample ARMT Questions Sample ARMT Questions ContCont
3355 3 388 3 322
3 3 3 333
Simplify the top simplify the bottom and then divideSimplify the top simplify the bottom and then divideSince the bases are the same throughout the whole Since the bases are the same throughout the whole
problem we know that the base of our answer will be 3 problem we know that the base of our answer will be 3 The top gives us 3The top gives us 35+8+25+8+2 = 3 = 31515
The bottom gives us 3The bottom gives us 31+31+3 = 3 = 344
Last we divide We keep the base of 3 and subtract the Last we divide We keep the base of 3 and subtract the exponents 15 ndash 4 = 11 Our answer is 3exponents 15 ndash 4 = 11 Our answer is 31111
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Rules for DivisionRules for Division
When you divide monomials and When you divide monomials and their bases are the same you their bases are the same you keep the base and subtract the keep the base and subtract the exponentsexponents
Example bExample b1010 divide b divide b33 = b = b10-310-3 = b = b77
Example 6Example 655 divide 6 = 6 divide 6 = 65-15-1 = 6 = 644
Independent Independent PracticePractice
A wA w1212 divide w divide w55
B pB p66 divide p divide p44
C 9C 97 7 divide 9divide 922
AnswersAnswersAA ww77
BB pp22
CC 9955
Sample ARMT Sample ARMT QuestionsQuestions SimplifySimplify 661010 divide (6 divide (677 divide 6 divide 622)) Following the order of operations we would Following the order of operations we would
take care of the parenthesis first Since both take care of the parenthesis first Since both bases are 6 we keep the base and subtract bases are 6 we keep the base and subtract (because we are dividing) 7-2 = 5 Then we (because we are dividing) 7-2 = 5 Then we have 6have 61010 divided by 6 divided by 655 We have the same We have the same base so we keep it and subtract 10 - 5 = 5 base so we keep it and subtract 10 - 5 = 5 Our answer is 6Our answer is 655
Sample ARMT Questions Sample ARMT Questions ContCont
3355 3 388 3 322
3 3 3 333
Simplify the top simplify the bottom and then divideSimplify the top simplify the bottom and then divideSince the bases are the same throughout the whole Since the bases are the same throughout the whole
problem we know that the base of our answer will be 3 problem we know that the base of our answer will be 3 The top gives us 3The top gives us 35+8+25+8+2 = 3 = 31515
The bottom gives us 3The bottom gives us 31+31+3 = 3 = 344
Last we divide We keep the base of 3 and subtract the Last we divide We keep the base of 3 and subtract the exponents 15 ndash 4 = 11 Our answer is 3exponents 15 ndash 4 = 11 Our answer is 31111
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Independent Independent PracticePractice
A wA w1212 divide w divide w55
B pB p66 divide p divide p44
C 9C 97 7 divide 9divide 922
AnswersAnswersAA ww77
BB pp22
CC 9955
Sample ARMT Sample ARMT QuestionsQuestions SimplifySimplify 661010 divide (6 divide (677 divide 6 divide 622)) Following the order of operations we would Following the order of operations we would
take care of the parenthesis first Since both take care of the parenthesis first Since both bases are 6 we keep the base and subtract bases are 6 we keep the base and subtract (because we are dividing) 7-2 = 5 Then we (because we are dividing) 7-2 = 5 Then we have 6have 61010 divided by 6 divided by 655 We have the same We have the same base so we keep it and subtract 10 - 5 = 5 base so we keep it and subtract 10 - 5 = 5 Our answer is 6Our answer is 655
Sample ARMT Questions Sample ARMT Questions ContCont
3355 3 388 3 322
3 3 3 333
Simplify the top simplify the bottom and then divideSimplify the top simplify the bottom and then divideSince the bases are the same throughout the whole Since the bases are the same throughout the whole
problem we know that the base of our answer will be 3 problem we know that the base of our answer will be 3 The top gives us 3The top gives us 35+8+25+8+2 = 3 = 31515
The bottom gives us 3The bottom gives us 31+31+3 = 3 = 344
Last we divide We keep the base of 3 and subtract the Last we divide We keep the base of 3 and subtract the exponents 15 ndash 4 = 11 Our answer is 3exponents 15 ndash 4 = 11 Our answer is 31111
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Sample ARMT Sample ARMT QuestionsQuestions SimplifySimplify 661010 divide (6 divide (677 divide 6 divide 622)) Following the order of operations we would Following the order of operations we would
take care of the parenthesis first Since both take care of the parenthesis first Since both bases are 6 we keep the base and subtract bases are 6 we keep the base and subtract (because we are dividing) 7-2 = 5 Then we (because we are dividing) 7-2 = 5 Then we have 6have 61010 divided by 6 divided by 655 We have the same We have the same base so we keep it and subtract 10 - 5 = 5 base so we keep it and subtract 10 - 5 = 5 Our answer is 6Our answer is 655
Sample ARMT Questions Sample ARMT Questions ContCont
3355 3 388 3 322
3 3 3 333
Simplify the top simplify the bottom and then divideSimplify the top simplify the bottom and then divideSince the bases are the same throughout the whole Since the bases are the same throughout the whole
problem we know that the base of our answer will be 3 problem we know that the base of our answer will be 3 The top gives us 3The top gives us 35+8+25+8+2 = 3 = 31515
The bottom gives us 3The bottom gives us 31+31+3 = 3 = 344
Last we divide We keep the base of 3 and subtract the Last we divide We keep the base of 3 and subtract the exponents 15 ndash 4 = 11 Our answer is 3exponents 15 ndash 4 = 11 Our answer is 31111
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Sample ARMT Questions Sample ARMT Questions ContCont
3355 3 388 3 322
3 3 3 333
Simplify the top simplify the bottom and then divideSimplify the top simplify the bottom and then divideSince the bases are the same throughout the whole Since the bases are the same throughout the whole
problem we know that the base of our answer will be 3 problem we know that the base of our answer will be 3 The top gives us 3The top gives us 35+8+25+8+2 = 3 = 31515
The bottom gives us 3The bottom gives us 31+31+3 = 3 = 344
Last we divide We keep the base of 3 and subtract the Last we divide We keep the base of 3 and subtract the exponents 15 ndash 4 = 11 Our answer is 3exponents 15 ndash 4 = 11 Our answer is 31111
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Sample ARMT Questions Sample ARMT Questions ContCont
Shelly drew a square and marked Shelly drew a square and marked the lengths of the sides using the lengths of the sides using exponential notation She then exponential notation She then wrote the expression 4wrote the expression 455 x 4 x 455 to to represent the area of the squarerepresent the area of the square
What is equivalent to the area in What is equivalent to the area in square units of Shellyrsquos squaresquare units of Shellyrsquos square
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
Sample ARMT Questions Sample ARMT Questions ContCont
45
45
To find the area of the square just multiply the length times the width 45 x 45 = 45+5 = 410
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents
ConclusionConclusion When dealing with monomials When dealing with monomials
remember to be MADS about remember to be MADS about monomials monomials
When you Multiply you Add the When you Multiply you Add the exponentsexponents
When you Divide you Subtract When you Divide you Subtract the exponentsthe exponents