Question

Solve each division problem, and classify it based on its quotient. a) 21 ÷ 7/3 =b) 4 2/3 ÷7/9=c) 12/7÷2/7 =d) 4 1/2÷1/2=e) 72/7 ÷ 8/7=f) 9 ÷ 3/2 =

Answer 1

To solve each of the given problems we will use the following properties of multiplication and division of fraction:

`\begin{gathered} (a)/(b)*(d)/(c)=(a* d)/(b* c) \\ \\ ((a)/(b))/((d)/(c))=(a)/(b)*(c)/(d) \\ \\ A(B)/(C)=(A* C+B)/(C) \end{gathered}`

To solve the problem a) we do as follows:

`(21)/((7)/(3))=((21)/(1))/((7)/(3))=(21)/(1)*(3)/(7)=(21*3)/(1*7)=(63)/(7)=9`

From this solution, the answer for problem a) is 9

For the problem b), we proceed as follows:

`\begin{gathered} (4(2)/(3))/((7)/(9))=((4*3+2)/(3))/((7)/(9)) \\ \\ =((14)/(3))/((7)/(9)) \\ \\ =(14)/(3)*(9)/(7) \\ \\ =(14*9)/(3*7) \\ \\ =(2*7*3*3)/(3*7) \\ \\ =2*3=6 \end{gathered}`

From this solution, the answer for problem b) is 6

For the problem in the question c), we proceed as follows:

`((12)/(7))/((2)/(7))=(12)/(7)*(7)/(2)=(12*7)/(7*2)=(12)/(2)=6`

From this solution, the answer for problem c) is 6

Now, for the problem d), we proceed as follows:

`(4(1)/(2))/((1)/(2))=((4*2+1)/(2))/((1)/(2))=((8+1)/(2))/((1)/(2))=((9)/(2))/((1)/(2))=(9)/(2)*(2)/(1)=(9*2)/(2*1)=9`

From this solution, the answer for problem d) is 9

To solve the problem e), we proceed as follows:

`((72)/(7))/((8)/(7))=(72)/(7)*(7)/(8)=(72*7)/(7*8)=(72)/(8)=9`

From this solution, the answer for problem e) is 9

To solve the problem f), we proceed as follows:

`(9)/((3)/(2))=((9)/(1))/((3)/(2))=(9)/(1)*(2)/(3)=(9*2)/(1*3)=(18)/(3)=6`

From this solution, the answer for problem f) is 6