Of the following, which is the greatest?

Question

A.  \frac{7}{9}

B.  \frac{5}{7}

C.  (\frac{7}{9})^2

D.  (\frac{5}{7})^3

E.  (\frac{7}{9})^3

gchandana · Answer

Official Explanation

Usernamevisible · Answer

You need to know fraction 
1/9 is 0.1111
and 
1/7 = 0.1428

Now 7/9 = 0.77 and 5/9 = (14*5=70) = ~0.7

Thus 7/9 is greater

Now for B,C and D
in fraction squaring and cubing always result into lower number

Thus A

Bunuel · Answer

Of the following, which is the greatest?

A. \(\frac{7}{9}\)

B. \(\frac{5}{7}\)

C. \((\frac{7}{9})^2\)

D. \((\frac{5}{7})^3\)

E. \((\frac{7}{9})^3\)

The fractions \(\frac{7}{9}\) and \(\frac{5}{7}\) are both between 0 and 1, so raising either of them to a power makes it smaller.

Thus, the powered options are smaller than their original fractions.

Now compare \(\frac{7}{9}\) and \(\frac{5}{7}\).

Use the common denominator 63:

\(\frac{7}{9} = \frac{49}{63}\)

\(\frac{5}{7} = \frac{45}{63}\)

Since \(\frac{49}{63} > \frac{45}{63}\), we have \(\frac{7}{9} > \frac{5}{7}\).

Therefore, \(\frac{7}{9}\) is the greatest value.

Answer: A.

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MartyMurray · Answer

Of the following, which is the greatest?

A.  \frac{7}{9}

B.  \frac{5}{7}

C.  (\frac{7}{9})^2

D.  (\frac{5}{7})^3

E.  (\frac{7}{9})^3

A positive fraction less than 1 raised to a power is smaller than the original fraction.

So,  \frac{7 }{9}  and  \frac{5}{7 }  are both greater than either of them raised to a power in (C), (D), or (E).

Thus, we are down to (A) and (B).

\frac{7}{9}  is  \frac{2}{9}  less than  \frac{9}{9} = 1 .

\frac{5}{7}  is  \frac{2}{7}  less than  \frac{7}{7} = 1

Thus, since  \frac{1}{9} < \frac{1}{7}  ,  \frac{7}{9}  is closer to 1 than  \frac{5}{ 7} .

So,  \frac{7}{9}  >  \frac{5}{7} .

Correct answer:   A

Of the following, which is the greatest?

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Of the following, which is the greatest?

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615 to 715 in 15 Days (Ria's Strategies)

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