I think you would like to recheck your calculation for quantity A

\((\frac{1}{4})\%\) of 100 is \(\frac{1}{400}\times 100 = 0.25\)

First thing I did was pick a number. x=10
A: 1/4=0.25. So 1/4%= 0.25/100. Therefore: 10*0.25*25/100*100 I just clubbed the whole thing. When you simplify it = 1/160
B: 1/16th of 10*10/100. When you simplify it = 1/16

There are lot of ways to do this I guess. I do not think there is any particular time-saving method. Just figure out what you understand better and what works for you best. I work better by picking numbers while others could do it just using the variable.

It said (1/4)% which means one by forth per cent = 1/4 divided by 100 = 0.25/100
therefore,
= (100 * 0.25/100) * 0.25
= 0.0625

\(\text{ Since x>0 }\)

\(25 \text{ % }\) = \(\frac{1}{4}\)

\(\frac{1}{4} \text{ % }\) = \(\frac{1}{400}\)

Quantity A

\(\frac{1}{4} \times \frac{1}{400}\)

\(\frac{1}{1600}\)

Quantity B

\(\frac{1}{16} \times \frac{10}{100}\)

\(\frac{1}{160}\)

Clearly \(\frac{1}{160} > \frac{1}{1600}\)

Therefore Quantity B is greatest.

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