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Which of the following fractions has the greatest value?
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15 Jul 2019, 16:17
15 Jul 2019, 16:17
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Which of the following fractions has the greatest value?
A. \(\frac{7}{16 \times 25}\)
B. \(\frac{5}{32 \times 5^4}\)
C. \(\frac{30}{512 \times 5^3}\)
D. \(\frac{5}{4^6 \times 5}\)
E. \(\frac{4}{2^{11}\times 5^2}\)
A. \(\frac{7}{16 \times 25}\)
B. \(\frac{5}{32 \times 5^4}\)
C. \(\frac{30}{512 \times 5^3}\)
D. \(\frac{5}{4^6 \times 5}\)
E. \(\frac{4}{2^{11}\times 5^2}\)
Re: Which of the following fractions has the greatest value?
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17 Jul 2019, 09:29
17 Jul 2019, 09:29
Hello Sir Brent, can you please suggest us how should we approach these type of question? it seems too much time consuming for me.
Thanks,
Alamin
Thanks,
Alamin
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Which of the following fractions has the greatest value?
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17 Jul 2019, 10:46
17 Jul 2019, 10:46
1
Carcass wrote:
Which of the following fractions has the greatest value?
A. \(\frac{7}{16 \times 25}\)
B. \(\frac{5}{32 \times 5^4}\)
C. \(\frac{30}{512 \times 5^3}\)
D. \(\frac{5}{4^6 \times 5}\)
E. \(\frac{4}{2^{11}\times 5^2}\)
A. \(\frac{7}{16 \times 25}\)
B. \(\frac{5}{32 \times 5^4}\)
C. \(\frac{30}{512 \times 5^3}\)
D. \(\frac{5}{4^6 \times 5}\)
E. \(\frac{4}{2^{11}\times 5^2}\)
Most of the denominators are a pain to calculate.
HOWEVER, the first one (A) is reasonable.
A. \(\frac{7}{16 \times 25}=\frac{7}{400}\)
Now, let's check the remaining answer choices....
B. \(\frac{5}{32 \times 5^4}\)
5^4 (which we should memorize before test day) = 625
So, the denominator is already a lot bigger than 400, which means this fraction is definitely LESS THAN \(\frac{7}{400}\)
C. \(\frac{30}{512 \times 5^3}\)
Same scenario here.
5^3 = 125, so the denominator here is (512)(125), which is HUGE.
So, even with 30 as the numerator, this fraction is definitely LESS THAN \(\frac{7}{400}\)
D. \(\frac{5}{4^6 \times 5}\)
4^6 = (4^3)(4^3)
= (64)(64)
= some number BIGGER than 3600
That's already a huge denominator, which means this fraction is definitely LESS THAN \(\frac{7}{400}\)
E. \(\frac{4}{2^{11}\times 5^2}\)
2^11 = 2048
I'll stop right there, since we can already see that this fraction is definitely LESS THAN \(\frac{7}{400}\)
Answer: A
