How do you calculate volume with cubes of fraction lengths?

I'm doing some exercises on Khanacademy.org and I keep having trouble with one exercise. The questions are like this: how many $1/4$cm cubes does it take to fill a prism if the prism is $1$cm $\times$ $7/4$cm $\times$ $2$cm? I consistently get these wrong and Khan academy's explanations aren't working for me. I've tried converting all the side lengths to multiples(?) of $1/4$, such as $4/4 \times 7/4 \times 8/4$ and multiplying but I still get the wrong answer. How do I calculate this?

• Converting to units of $1/4$ cm makes sense. Edit the question to show your work and we can look for your mistake. – Ethan Bolker Jan 29 '18 at 0:20
• @EthanBolker i believe the OPs error already shows: after converting, he multiplies the sides as converted, giving the same result as just multiplying them in the beginning. – RGS Jan 29 '18 at 0:22

1 Answer

You have to find for each side, independently, how many cubes would fit in that side.

$1/4$ fits $4$ times in the side $1$.

$1/4$ fits $7$ times in the side $7/4$.

$1/4$ fits $8$ times in the side $2$.

The answer is then $4\times7\times8 = 224$

Another way of answering would be by starting to write everything in multiples of $1/4$ like you did, and then remove all the $/4$ from the denominators. That would leave you with the question:

How many cubes of side $1$ fit into a rectangle of sides $4\times7\times8$? And then yes, you multiply.

• Great, thanks. I just tried the exercise again and got them all right. – Userq49874 Jan 29 '18 at 0:37
• @WebUserLearner Glad I could help; I am a great fan and a usual user of KhanAcademy myself ;) – RGS Jan 29 '18 at 0:38