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02 Dec 2021, 04:47
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Of the following, which is least?
A. \(\frac{-0.7}{0.000012}\)
B. \(\frac{0.7}{-0.00012}\)
C. \(-\frac{0.7}{0.0012}\)
D. \((\frac{0.012}{-0.7})^{-1}\)
E. \(-\frac{0.7}{0.12}\)
A. \(\frac{-0.7}{0.000012}\)
B. \(\frac{0.7}{-0.00012}\)
C. \(-\frac{0.7}{0.0012}\)
D. \((\frac{0.012}{-0.7})^{-1}\)
E. \(-\frac{0.7}{0.12}\)
02 Dec 2021, 04:47
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Official Solution:
Of the following, which is least?
A. \(\frac{-0.7}{0.000012}\)
B. \(\frac{0.7}{-0.00012}\)
C. \(-\frac{0.7}{0.0012}\)
D. \((\frac{0.012}{-0.7})^{-1}\)
E. \(-\frac{0.7}{0.12}\)
Firs of all notice that all the numbers are negative and we can re-write all of them so that the numerator is the same: \(0.7\):
A. \(\frac{-0.7}{0.000012}=\frac{0.7}{-0.000012}\)
B. \(\frac{0.7}{-0.00012}\)
C. \(-\frac{0.7}{0.0012}=\frac{0.7}{-0.0012}\)
D. \((\frac{0.012}{-0.7})^{-1}=\frac{-0.7}{0.012}=\frac{0.7}{-0.012}\)
E. \(-\frac{0.7}{0.12}=\frac{0.7}{-0.12}\)
Each option is of the form \(\frac{0.7}{negative}\). For such fractions, larger the denominator (so closer the negative number in the denominator is to zero), the smaller the fraction (for example, \(-1 > -10\), thus \( (\frac{10}{-1} = -10) < (\frac{10}{-10} = -1) \)).
The largest denominator is in option A (\(-0.000012\)), so it has the least value.
Answer: A
Of the following, which is least?
A. \(\frac{-0.7}{0.000012}\)
B. \(\frac{0.7}{-0.00012}\)
C. \(-\frac{0.7}{0.0012}\)
D. \((\frac{0.012}{-0.7})^{-1}\)
E. \(-\frac{0.7}{0.12}\)
Firs of all notice that all the numbers are negative and we can re-write all of them so that the numerator is the same: \(0.7\):
A. \(\frac{-0.7}{0.000012}=\frac{0.7}{-0.000012}\)
B. \(\frac{0.7}{-0.00012}\)
C. \(-\frac{0.7}{0.0012}=\frac{0.7}{-0.0012}\)
D. \((\frac{0.012}{-0.7})^{-1}=\frac{-0.7}{0.012}=\frac{0.7}{-0.012}\)
E. \(-\frac{0.7}{0.12}=\frac{0.7}{-0.12}\)
Each option is of the form \(\frac{0.7}{negative}\). For such fractions, larger the denominator (so closer the negative number in the denominator is to zero), the smaller the fraction (for example, \(-1 > -10\), thus \( (\frac{10}{-1} = -10) < (\frac{10}{-10} = -1) \)).
The largest denominator is in option A (\(-0.000012\)), so it has the least value.
Answer: A
