Question 33994
<pre><font size = 4><b>If a can of apple juice holds 12 ounces, a case of 24 cans would 
be how many quarts of juice? 
 
Dimensional analysis:

We will change the unit "cans" to "ounces" and then change
the unit "ounces" to "quarts".

We start with 24 cans.  We make a fraction by putting it over 1

24 cans
———————
   1

Now we create a fraction to multiply that by. It will have "ounces"
on the top and "cans" on the bottom:

24 cans   __ ounces  
——————— × —————————
   1       __ cans

Since 1 can = 12 ounces, we fill in the blank by "ounces" with 12 and
the blank by "cans" with 1.

24 cans   12 ounces  
——————— × —————————
   1        1 cans

Now we can cancel the "cans", and have only ounces:

24 <s>cans</s>   12 ounces  
——————— × —————————
   1        1 <s>cans</s>

Next we create a fraction to multiply that by. It will have 
quarts on the top and ounces on the bottom:

24 <s>cans</s>   12 ounces   __ quarts
——————— × ————————— × ——————————— 
   1        1 <s>cans</s>    __ ounces

Since 1 quart = 32 ounces, we fill in the blank by quarts 
with 1 and the blank by ounces with 32.

24 <s>cans</s>   12 ounces     1 quarts
——————— × ————————— × ————————————
   1        1 <s>cans</s>     32 ounces

Now we can cancel the ounces, and have only quarts left:

24 <s>cans</s>   12 <s>ounces</s>     1 quarts
——————— × ————————— × ————————————
   1        1 <s>cans</s>     32 <s>ounces</s>

Indicate the numbers multiplied on the top and the bottom, and
eliminate the canceled units:

24×12×1 quarts
——————————————
   1×1×32

8 will divide into 24 and also into 32

 3
<s>24</s>×12×1 quarts
——————————————
   1×1×<s>32</s>
        4

The 4 on the bottom will cancel into the 12 on the top:

 3  3
<s>24</s>×<s>12</s>×1 quarts
——————————————
   1×1×<s>32</s>
        <s>4</s>
        1

So we end up with 3×3 quarts or 9 quarts.

Edwin
AnlytcPhil@aol.com</pre>