Question

Which is the best reason why 3/5 is the exact quotient for 1/2 divided by 5/6

Answer 1

In your picture, the bottom right answer (3/5 times 5/6 = 1/2)

Answer 2

We are asked to choose the reason why
`(3)/(5)` is the exact quotient for
`(1)/(2)` divided by
`(5)/(6)`.

We know that divisor is the number that we divide with. The quotient is the answer to any division problem. Dividend is the number that we want to divide.

`\text{Dividend}=\text{Quotient}* \text{Divisor}`

We can see that is our given problem dividend is
`(1)/(2)`, quotient is
`(3)/(5)` and divisor is
`(5)/(6)`. Upon multiplying quotient with divisor, we will get:

`\text{Dividend}=(3)/(5)* (5)/(6)`

We can cancel out 5 from numerator and denominator.

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

`(1)/(2)=(3)/(6)`

`(1)/(2)=(3* 1)/(3* 2)`

`(1)/(2)=(1)/(2)`

Since both sides are equal, therefore, last option
`(3)/(5)* (5)/(6)=(1)/(2)` is the correct choice.