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Which of the following fractions is closest to 1/2?

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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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01 Nov 2018, 17:58
Of all the explanations I read, I feel the below one is the best one.

Since we need to find out what's closest to 1/2, just subtract that from each of the options.

(A) 4/7 - 1/2 = 1/7
(B) 5/9 - 1/2 = 1/18
(C) 6/11 - 1/2 = 1/22
(D) 7/13 - 1/2 = 1/26
(E) 9/16 - 1/2 = 2/32 => 1/16

From the above since 1/26 is the lowest number, (D) is the correct answer.
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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01 Nov 2018, 19:03
amitkumarchandan wrote:
There are 4 ways to solve the problem (Which is also basically a summary to above explanations):
1. Calculate the decimal and find the answer: This should be used when the numbers are small or calculation is easy.
2. Subtract the number (1/2 in this case) one by one with all the options to find the distance between those numbers, the smallest value would mean the closest number. (My favorite)
3. Use algebra to solve the arithmetic: To be used cautiously after identifying the pattern enabling algebraic equation formation.
4. Divide the options with the given number to see which number is closest to 1 (1 because we will also be dividing the given number, 1/2 in this case, to the same number)

My favorite as well!!

Of all the explanations I read, I feel the below one is the best one.

Since we need to find out what's closest to $$\frac{1}{2}$$, just subtract that from each of the options.

(A) $$\frac{4}{7}$$ - $$\frac{1}{2}$$ = $$\frac{1}{7}$$
(B) $$\frac{5}{9}$$ - $$\frac{1}{2}$$ = $$\frac{1}{18}$$
(C) $$\frac{6}{11}$$ - $$\frac{1}{2}$$ = $$\frac{1}{22}$$
(D) $$\frac{7}{13}$$ - $$\frac{1}{2}$$ = $$\frac{1}{26}$$
(E) $$\frac{9}{16}$$ - $$\frac{1}{2}$$ = $$\frac{2}{32}$$ => $$\frac{1}{16}$$

From the above since $$\frac{1}{26}$$ is the lowest number, (D) is the correct answer.
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Which of the following fractions is closest to 1/2?  [#permalink]

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21 Apr 2019, 09:24
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Which of the following fractions is closest to $$\frac{1}{2}$$?
A) $$\frac{4}{7}$$
B) $$\frac{5}{9}$$
C) $$\frac{6}{11}$$
D) $$\frac{7}{13}$$
E) $$\frac{9}{16}$$

To determine which answer choice is closest to 1/2, we can subtract 1/2 from each answer choice. The difference that is closest to zero will indicate the fraction that is closest to 1/2.

A) 4/7

4/7 - 1/2 = 8/14 - 7/14 = 1/14

B) 5/9

5/9 - 1/2 = 10/18 - 9/18 = 1/18

C) 6/11

6/11 - 1/2 = 12/22 - 11/22 = 1/22

D) 7/13

7/13 - 1/2 = 14/26 - 13/26 = 1/26

E) 9/16

9/16 - 1/2 = 9/16 - 8/16 = 1/16

Since 1/26 is closest to zero, 7/13 is closest to 1/2.

ScottTargetTestPrep /VeritasKarishma. Kindly help. If the Options include the following three:

1. 5/11
2. 50/99
3. 50/101.

Then with the above approach I am getting two negative values (For 1 and 3). Should I ignore the negative sign and focus on largest denominator ? So that the largest denominator can be the ans.
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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21 Apr 2019, 21:36
1
MBA20 wrote:
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Which of the following fractions is closest to $$\frac{1}{2}$$?
A) $$\frac{4}{7}$$
B) $$\frac{5}{9}$$
C) $$\frac{6}{11}$$
D) $$\frac{7}{13}$$
E) $$\frac{9}{16}$$

To determine which answer choice is closest to 1/2, we can subtract 1/2 from each answer choice. The difference that is closest to zero will indicate the fraction that is closest to 1/2.

A) 4/7

4/7 - 1/2 = 8/14 - 7/14 = 1/14

B) 5/9

5/9 - 1/2 = 10/18 - 9/18 = 1/18

C) 6/11

6/11 - 1/2 = 12/22 - 11/22 = 1/22

D) 7/13

7/13 - 1/2 = 14/26 - 13/26 = 1/26

E) 9/16

9/16 - 1/2 = 9/16 - 8/16 = 1/16

Since 1/26 is closest to zero, 7/13 is closest to 1/2.

ScottTargetTestPrep /VeritasKarishma. Kindly help. If the Options include the following three:

1. 5/11
2. 50/99
3. 50/101.

Then with the above approach I am getting two negative values (For 1 and 3). Should I ignore the negative sign and focus on largest denominator ? So that the largest denominator can be the ans.

Closest to 1/2 could be slightly less than 1/2 or slightly more than 1/2. When you subtract 1/2, the number slightly less than 1/2 will become negative. Still, we need to be as close to 0 as possible i.e. distance from 0 to be as small as possible. Basically, the absolute value of the number obtained should be as small as possible. So you ignore the sign you get and focus on just the absolute value. It should be smallest (with same numerator, the denominator should be greatest).
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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23 Apr 2019, 15:05
1
MBA20 wrote:
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Which of the following fractions is closest to $$\frac{1}{2}$$?
A) $$\frac{4}{7}$$
B) $$\frac{5}{9}$$
C) $$\frac{6}{11}$$
D) $$\frac{7}{13}$$
E) $$\frac{9}{16}$$

To determine which answer choice is closest to 1/2, we can subtract 1/2 from each answer choice. The difference that is closest to zero will indicate the fraction that is closest to 1/2.

A) 4/7

4/7 - 1/2 = 8/14 - 7/14 = 1/14

B) 5/9

5/9 - 1/2 = 10/18 - 9/18 = 1/18

C) 6/11

6/11 - 1/2 = 12/22 - 11/22 = 1/22

D) 7/13

7/13 - 1/2 = 14/26 - 13/26 = 1/26

E) 9/16

9/16 - 1/2 = 9/16 - 8/16 = 1/16

Since 1/26 is closest to zero, 7/13 is closest to 1/2.

ScottTargetTestPrep /VeritasKarishma. Kindly help. If the Options include the following three:

1. 5/11
2. 50/99
3. 50/101.

Then with the above approach I am getting two negative values (For 1 and 3). Should I ignore the negative sign and focus on largest denominator ? So that the largest denominator can be the ans.

In the original example, all the given answer choices were greater than 1/2; that’s why we didn’t bother with absolute values and just subtracted 1/2 from each answer choice. In reality, if some of the answer choices were greater than 1/2 and some were less, we would compare the absolute value of the difference of the numbers and 1/2. The reason for that has to do with distances on the real number line; the distance between two real numbers is the absolute value of their difference. So, for the numbers you provided, you should compare the absolute values of the distances and take the one closest to zero. Another way of saying that is for the ones greater than 1/2, subtract 1/2 and for the ones less than 1/2, subtract those numbers from 1/2.
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Which of the following fractions is closest to 1/2?  [#permalink]

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09 May 2019, 01:49
AbdurRakib wrote:
Which of the following fractions is closest to $$\frac{1}{2}$$?

A) $$\frac{4}{7}$$

B) $$\frac{5}{9}$$

C) $$\frac{6}{11}$$

D) $$\frac{7}{13}$$

E) $$\frac{9}{16}$$

OG 2017 New Question

First, we'll multiply 100 with every fraction.

Approximate values:

A. 4/7*100=56

B. 5/9*100=55

C.6/11*100=54

D. 7/13*100=49 (correct)

E. 9/16*100=54

Because we know 1/2*100=50 which is closest to 49.

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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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09 Nov 2019, 02:00
I solved this by % method.
If we know a few fractions --> percentages conversions, it will be easier.
The Question asks - fraction closest to $$\frac{1}{2}$$--> 50%

Let analyze the options
A) $$\frac{4}{7}$$ -- $$4*\frac{1}{7}$$ = $$14.28 * 4$$ = $$57.something%$$ (Since, we know $$\frac{1}{7}$$ = 14.28%) - 57.14% to be precise

B) $$\frac{5}{9}$$ -- $$5*\frac{1}{9}$$ = $$11.11 * 5$$ = $$55.something%$$ (Since, we know $$\frac{1}{9}$$ = 11.11%) - 55.55% to be precise

C) $$\frac{6}{11}$$ -- $$6*\frac{1}{11}$$ = $$9.09 * 6$$ = $$54.something%$$ (Since, we know $$\frac{1}{11}$$ = 09.09%) - 54.54% to be precise

D) $$\frac{7}{13}$$ -- $$7*\frac{1}{13}$$ = $$7.67 * 7$$ = $$53.something%$$ (Since, we know $$\frac{1}{13}$$ = 07.67%) - 53.80% to be precise

E) $$\frac{9}{16}$$ -- $$9*\frac{1}{16}$$ = $$6.25 * 9$$ = $$56.something%$$ (Since, we know $$\frac{1}{16}$$ = 06.25%) - 56.25% to be precise

Clearly, Option A to Option E ranges from - 57, 55, 54, 53, 56 % respectively with 53% being the closest to 50%
Hence, our answer Option D $$\frac{7}{13}$$

Just for info below are some basic fraction to a percentage conversion
$$\frac{1}{1} = 100$$% ------ $$\frac{1}{2} = 50$$%

$$\frac{1}{3} = 33.33$$% ------ $$\frac{1}{4} = 25$$%

$$\frac{1}{5} = 20$$% ------ $$\frac{1}{6} = 16.67$$%

$$\frac{1}{7} = 14.28$$% ------ $$\frac{1}{8} = 12.25$$%

$$\frac{1}{9} = 11.11$$% ------ $$\frac{1}{10} = 10$$%

$$\frac{1}{11} = 09.09$$% ------ $$\frac{1}{12} = 8.33$$%

$$\frac{1}{13} = 7.67$$% ------ $$\frac{1}{14} = 7.14$$%

$$\frac{1}{15} = 7.33$$% ------ $$\frac{1}{16} = 6.25$$%

$$\frac{2}{5} = 40$$% ------ $$\frac{3}{5} = 60$$%

$$\frac{3}{4} = 75$$% ------ $$\frac{4}{5} = 80$$%
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Re: Which of the following fractions is closest to 1/2?  [#permalink]

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28 Nov 2019, 10:14
chetan2u wrote:
AbdurRakib wrote:
Which of the following fractions is closest to $$\frac{1}{2}$$?
A) $$\frac{4}{7}$$
B) $$\frac{5}{9}$$
C) $$\frac{6}{11}$$
D) $$\frac{7}{13}$$
E) $$\frac{9}{16}$$

OG 2017 New Question

Hi,

Do not waste time in calculating..
look at the similarity in all choices- they all EXCEPT E are of type $$\frac{x}{2x-1}$$...
and $$\frac{x}{2x-1}$$ for an integer x is always >1/2 and will become lesser in value , that is will keep getting closer to 1/2 with higher VALUE of x..

you can check in two ways-
1) for x as 1 or 2 or 3..
x=1, $$\frac{x}{2x-1}$$ = 1..
x=2, $$\frac{x}{2x-1}$$ = 2/3..
x=3, $$\frac{x}{2x-1}$$ = 3/5..
so each successive value is smaller than previous one..

2) simplify the term..- IMPORTANT
$$\frac{x}{2x-1}$$=$$\frac{1}{(2x-1)/x}$$ = $$\frac{1}{(2x/x-1/x)}$$ = $$\frac{1}{(2-1/x)}$$
so the denominator should be closer to 2 so $$2-\frac{1}{x}$$ should be close to 2, and therefore x should be MAX to make $$\frac{1}{x}$$ less

Therefore, here 7 is the highest value in the four choices so D is the closest to 1/2.

lets see E... It is the TYPE $$\frac{x}{2(x-1)}$$... clearly since 7 and 9 are close to each other but denominator in E is reduced by a larger number,

Can you help me understand this:
2) simplify the term..- IMPORTANT
x2x−1x2x−1=1(2x−1)/x1(2x−1)/x = 1(2x/x−1/x)1(2x/x−1/x) = 1(2−1/x)1(2−1/x)
so the denominator should be closer to 2 so 2−1x2−1x should be close to 2, and therefore x should be MAX to make 1x1x less
Re: Which of the following fractions is closest to 1/2?   [#permalink] 28 Nov 2019, 10:14

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