Question

What is the volume of the rectangular prism? Be sure to simplify

Answer 1

We are told that we want to calculate the volume of the rectangular prism. This can be calculated by simply multiplying the length of each dimension of the prism.

Note that in this case we have a height of 4/5, a base of 12 and a width of 1/4. So the volume would be

`(4)/(5)\cdot(1)/(4)\cdot12=(12\cdot1\cdot4)/(5\cdot4)=(12)/(5)`

Since this number doesn't concide with any of the given options, let us write it in its mixed fraction representation. To do so, we identify the denominator (5). Now we want to find the multiple of 5 that is the closes to 12 but it is strictly less than 12. We have that

5*2 = 10

and 5*3=15.

So we identify 10 as the closes multiple of 5 that is less than 12. Now we write

`(12)/(5)=(10+2)/(5)=(10)/(5)+(2)/(5)=2+(2)/(5)`

Note that in here we have a whole number of 2 and 2/5 as a fraction, so the mixed number representation would be

`(12)/(5)=2(2)/(5)`

which is the third option.