(01.07 MC) A carton has a length of fraction 2 and 2 over 3 feet, width of fraction 1 and 1 over 8 feet, and height of fraction 1 and 1 over 5 feet. What is the volume of the carton

Accepted Solution

Volume equals height x width x length. 
So your answer is 2 [tex] \frac{2}{3} [/tex] multiplied by 1 [tex] \frac{1}{8} [/tex] multiplied by 1 [tex] \frac{1}{5} [/tex] . 

The first thing to do is the convert all of these proper (whole number and fraction) fractions into improper fractions (one fraction that's over 1).

So, to convert 2 [tex] \frac{2}{3} [/tex], you have to multiply the whole number (2) by the denominator (3). Then add the numerator (2). 2*3=6+2=8. So your answer is 8/3, eight thirds.

Doing the same thing for all numbers gives you:
[tex] \frac{8}{3} , \frac{9}{8} , \frac{6}{5} [/tex] 

you can multiply these by multiplying all the numerators (the top numbers) together, to find the new numerator. 8*9*6=432.
Doing the same thing to find the denominator gives you 120. 

So the answer is 432 over 120. This number can be simplified by dividing by common factors. You can divide the two numbers by 2, for example, and it's a little more simple. Their largest common factor is 24 , though. Dividing each number by 24 means your answer (which is the same amount as 432/120) is [tex] \frac{18}{5} [/tex]. The proper fraction is 3 [tex] \frac{3}{5} [/tex], because 5 fits into 18 3 times. (3*5=15), but that leaves 3 left over. 

Since it's volume, the unit will be in cubic units ( a little 3 on the top). 
3 3/5 [tex] unit^{3} [/tex]