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 cans 12 ounces
——————— × —————————
1 1 cans
Next we create a fraction to multiply that by. It will have
quarts on the top and ounces on the bottom:
24 cans 12 ounces __ quarts
——————— × ————————— × ———————————
1 1 cans __ ounces
Since 1 quart = 32 ounces, we fill in the blank by quarts
with 1 and the blank by ounces with 32.
24 cans 12 ounces 1 quarts
——————— × ————————— × ————————————
1 1 cans 32 ounces
Now we can cancel the ounces, and have only quarts left:
24 cans 12 ounces 1 quarts
——————— × ————————— × ————————————
1 1 cans 32 ounces
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
24×12×1 quarts
——————————————
1×1×32
4
The 4 on the bottom will cancel into the 12 on the top:
3 3
24×12×1 quarts
——————————————
1×1×32
4
1
So we end up with 3×3 quarts or 9 quarts.
Edwin
AnlytcPhil@aol.com