Which of the following is the largest?

Question

A)  \frac{−8}{31}

B)  \frac{ −9}{34}

C)  \frac{−10}{37}

D)  \frac{−11}{40}

E)  \frac{−12}{43}

chetan2u · Accepted Answer

The smallest value of the MOD of options is the answer. Let us convert them in terms of x.

A)  \frac{−8}{31}=|\frac{8}{31}|=|\frac{8}{32-1}|=|\frac{8}{4*8-1}|=|\frac{x}{4x-1}|

B) \frac{ −9}{34}=|\frac{9}{34}|=|\frac{9}{36-2}|=|\frac{9}{4*9-2}|=|\frac{x}{4x-2}|

C)  \frac{−10}{37}=|\frac{10}{37}|=|\frac{10}{40-3}|=|\frac{10}{4*10-3}|=|\frac{x}{4x-3}|

D)  \frac{−11}{40}=|\frac{11}{40}|=|\frac{11}{44-4}|=|\frac{11}{4*11-4}|=|\frac{x}{4x-4}|

E)  \frac{−12}{43}=|\frac{12}{43}|=|\frac{12}{48-1}|=|\frac{12}{4*12-5}|=|\frac{x}{4x-5}|

Now, in all above, the numerator is the same, that is x.
Therefore, the one with the largest denominator will be the smallest:  (4x-5)<(4x-4)<(4x-3)<(4x-2)<(4x-1) 
Since 4x-1 is the largest,  |\frac{x}{4x-1}|  will be the smallest and  -\frac{x}{4x-1}   will be the largest.

Thus  \frac{−8}{31}  is the largest.

A

CEdward · Answer

Best thing to do here is ignore the negatives and find the smallest number. That will be the choice that is least negative.

A.

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ScottTargetTestPrep · Answer

Solution:
 
Since all the numbers are negative, let’s compare their absolute values. Keep in mind that the negative number that has the smallest absolute value is the largest. We can also observe that, in terms of the absolute value of the numbers, the numerator is increasing by 1 and the denominator is increasing by 3 from one choice to the next. Therefore, we can just compare choices A and B. If choice A’s absolute value is less than that of choice B, then choice A’s number is the largest. On the other hand, If choice A’s absolute value is greater than that of choice B, then choice E’s number is the largest.

8/31 < 9/34 ?

8 x 34 < 9 x 31 ?

272 < 279 ? → Yes

We see that -8/31 has the smallest absolute value, therefore, it is the largest.

Answer: A

MathRevolution · Answer

The numerator is getting smaller and the denominator is increasing which will make the fraction smaller.

A will be the largest.

Answer A

Russ19 · Answer

Official Explanation:

It will be easier to compare positive values, and if we make every fraction positive, we will want instead to know which fraction is smallest (because that fraction will become largest if made negative). Making the answers positive, notice that when we go from answer A, 8/31, to answer B, 9/34, we are adding 1 to the numerator and 3 to the denominator. When we do this, the overall value of the fraction will get closer to 1/3. Since 8/31 is less than 1/3 (it is very close in value to 8/32=1/4), when we add 1 to its numerator and 3 to its denominator, the overall value of the fraction will get bigger. But the same will be true for each subsequent fraction since as we progress through the five answer choices, we increase the numerator by 1 and the denominator by 3 each
time. So
8/31< 9/34 <10/37 <11/40 < 12/43 and thus

−8/31 > −9/34 > −10/37 > −11/40> −12/43

and the answer is A.

Mingyue-0810 · Answer

The values are negtive, so smallest number will be larger.

A

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bumpbot · Answer

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Which of the following is the largest?

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Which of the following is the largest?

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