Which of the following fractions is the smallest?

Question

A. 3/10.
B. 6/19.
C. 3/8.
D. 11/30.
E. 12/31.

GeorgeKo111 · Answer

Solution:
i will break the solution into 3 parts and eliminate obvious wrong answers:
part 1:
given:
A) 3/10= 6/20 and c) 3/8= 6/16 and we have B)given = 6/19. between these 3 fractions it is now obvious that 3/10 is the smallest so we eliminate B and C. and we keep A.

part 2: we compare D and E using bow method:

11x31= 341 and 30x12= 360 ---> 360>341 ---> 12/31 > 11/30 so we eliminate choice E)

part 3:

now we compare the two left choices A and D using the bow method:

3x30= 90 and 10x11=110 ---> 110>90 ---> 11/30>3/10

or we can multiply choice A by 3 and compare it to D:

(3/10)x 3 = 9/30 and 9/30<11/30 then A is the smallest choice.

chrtpmdr · Answer

My approach:

List the numbers up from 3/10 - 6/19 - 3/8 - 11/30 - 12 / 31

Look for the pattern - obviously they want something from us that involves 1/3 because all numbers are suspiciously close to 1/3 
So let's check

3/10 = 0,30 -> another way to check is to perform 3*3 which is 9 and means it is slightly smaller then 1/3 
6/19 = x -> 6*3 = 18 so this one is slightly smaller than 1/3 as well

Now with the following three you immediately are going to recognize that all of the numbers *3 lead to something greater then the whole fraction, which means all of those numbers are greater then 1/3 and therefore can be eliminated.

With the last two numbers you probably have several options to check which one is larger / smaller, I just went with simple divsion. 
Because I already knew that 10/30 is 0.30 so I basically wrote 6/19 and immediately saw that it's something like 0.31xxxx

So therefore I choose a)

Correct me if wrong

Harsh9676 · Answer

IMO A

The easiest and the quickest way to find the largest or smallest fraction is to use this general rule that

a/b > c/d, if ad > bc

Using this and comparing A & B => AD (3*19) < BC (10*6) so A is less than B, so eliminate B

similarly Comparing A & C => AD (3*8) < BC (10*3) so A is less than C, so eliminate C

Comparing A & D => AD (3*30) < BC (10*11) so A is less than D, so eliminate D

Finally A& E => AD (3*31) < BC (10*12) so A is less than E, so eliminate E

Ans A

ScottTargetTestPrep · Answer

We can easily see that 3/8 (since it’s greater than 3/10) and 11/30 (since it’s greater than 3/10 = 9/30) are not the smallest, so we are left with 3/10, 6/19 and 12/31.

Since 3/10 = 6/20, we see that 3/10 is less than 6/19. Similarly, since 3/10 = 12/40, we see that 3/10 is less than 12/31. Therefore, 3/10 is the smallest.

Answer: A

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Which of the following fractions is the smallest?

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Which of the following fractions is the smallest?

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