IN2MBB2PE wrote:
Hi
AndrewN - Please explain if you can -
I understood the calculation part that how much Carol ate and that's how I came to the right answer but what I do not understand is that the question is asking for -
"the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?" Why don't we do an extra step after we know the total of her portion to find what fraction of a WHOLE extra-large sandwich she's eating?
Hello,
IN2MBB2PE. The answer to your question is that the two amounts are one and the same. As long as you keep your fractions straightened out, the partial amounts of each sandwich that she did eat will sum to an amount relative to one whole extra-large sandwich, whether there were 5 people, in which case your fraction will be slightly greater than 1—8/5 or 1 and 3/5
of one sandwich, to be exact—or, say, 24 people. Consider the latter case:
Sandwich #1 (evenly divided)—Carol eats 1/24 of the sandwich
Sandwich #2 (evenly divided)—Carol eats 1/24 of the sandwich
Sandwich #3 (evenly divided)—Carol eats 1/24 of the sandwich
Sandwich #4 (evenly divided among all but 4 students)—Carol eats 1/20 of the sandwich
\(\frac{1}{24} + \frac{1}{24} + \frac{1}{24} + \frac{1}{20}\)
\(3(\frac{1}{24}) + \frac{1}{20}\)
\(\frac{3}{24} + \frac{1}{20}\)
\(\frac{1}{8} + \frac{1}{20}\)
\(\frac{5}{40} + \frac{2}{40}\)
\(\frac{7}{40}\)
Of course, this 7/40 also uses
one sandwich as the benchmark, so no extra step, such as dividing the sum by 4, is needed. (We have already performed the necessary division on
each sandwich. The key here is that all the sandwiches are
of exactly the same size.)
Thank you for following up. Perhaps that makes more sense now. Good luck with your studies.
- Andrew