Question

Joaquin has been working on homework for 3 1/2 hours. If each assignment takes him of 1/4 an hour, how many assignments has he completed? Select one OA. 13 O B. 14 OC. 15 OD. 16

Answer 1

The total amount of time he has spent doing homework:

`3(1)/(2)`

And the time it takes to complete each assignment:

`(1)/(4)`

To find the number of assignments he has completed in that time, we divide the total time 3 1/2 by the time for each assignment 1/4:

`3(1)/(2)/(1)/(4)`

To make this division we need to convert 3 1/2 to a fraction as follows:

`3(1)/(2)=(3*2+1)/(2)=(6+1)/(2)=(7)/(2)`

We multiply the whole number by the denominator 3x2 and we add to that the numerator 1, and divide that by the original denominator 2.

Now instead of 3 1/2 we use 7/2 for our division:

`(7)/(2)/(1)/(4)`

And we use the formula to divide two fractions, which is:

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

Applying this to our division:

`(7)/(2)/(1)/(4)=(7*4)/(2*1)`

Solving the operations:

`(7)/(2)/(1)/(4)=(28)/(2)=14`

Answer: 14 assignments