Question

Hassan's bird feeder holds 5 5/6 cups of bird seeds. Hassin is feeling the bird feeder with a swoop that holds 5/6 of a cup.how many scoops of bird seeds will Hassan put into the feeder

Answer 1

Cups that the bird feeder holds:

`5(5)/(6)`

Cups that the scoop holds:

`(5)/(6)`

To solve this problem and find how many scoops are needed to fill the bird feeder, we need to divide the amount that the bird feeder holds by the amount that the scoop holds:

`(5(5)/(6))/((5)/(6))`

To make this division, convert the mixed number to a fraction using the following rule:

`A(b)/(c)=(A* c+b)/(c)`

Thus, we convert 5 5/6 to fraction:

`5(5)/(6)=(5*6+5)/(6)`

Solving the operations:

`\begin{gathered} 5(5)/(6)=(30+5)/(6) \\ 5(5)/(6)=(35)/(6) \end{gathered}`

In the original division we had:

`(5(5)/(6))/((5)/(6))`

We substitute 35/6 in the place of 5 5/6:

`((35)/(6))/((5)/(6))`

And to solve this division, we use the following rule:

`((a)/(b))/((c)/(d))=(a* d)/(b* c)`

--> Using that rule, the division we have to solve becomes:

`((35)/(6))/((5)/(6))=(35*6)/(6*5)`

Since we have 6 multiplying on the numerator and also on the denominator, they cancel each other and we get:

`((35)/(6))/((5)/(6))=(35)/(5)`

Finally, dividing 35/5 we get the result:

`(35)/(5)=7`

7 scoops are needed.

Answer: 7 scoops