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# Which of the following fractions is the largest?

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Math Expert
Joined: 02 Sep 2009
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Which of the following fractions is the largest? [#permalink]

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29 Oct 2017, 01:28
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Which of the following fractions is the largest?

A. 5/6

B. 11/14

C. 12/15

D. 17/21

E. 29/35
[Reveal] Spoiler: OA

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Which of the following fractions is the largest? [#permalink]

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29 Oct 2017, 11:53
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Bunuel wrote:
Which of the following fractions is the largest?

A. 5/6

B. 11/14

C. 12/15

D. 17/21

E. 29/35

LCM of denominators of all the fractions i.e LCM of 6, 14, 15, 21, 35 = 210

As a next stem we need to make all denominators equal to the LCM

A. $$\frac{5}{6} => \frac{5}{6}*\frac{35}{35}=\frac{175}{210}$$

B. $$\frac{11}{14} =>\frac{11}{14}*\frac{15}{15}=\frac{165}{210}$$

C. $$\frac{12}{15} =>\frac{12}{15}*\frac{14}{14}=\frac{168}{210}$$

D. $$\frac{17}{21} =>\frac{17}{21}*\frac{10}{10}=\frac{170}{210}$$

E. $$\frac{29}{35} => \frac{29}{35}*\frac{6}{6}=\frac{174}{210}$$

Clearly option A is the greatest

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Re: Which of the following fractions is the largest? [#permalink]

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30 Oct 2017, 08:28
Bunuel wrote:
Which of the following fractions is the largest?

A. 5/6

B. 11/14

C. 12/15

D. 17/21

E. 29/35

In order to compare fractions, take LCM of all denominators, 6,14,15,21,35.
LCM=210
A) $$\frac{5}{6}$$ = $$\frac{5*35}{6*35}$$=$$\frac{175}{210}$$
B) $$\frac{11}{14}$$ = $$\frac{11*15}{14*15}$$=$$\frac{165}{210}$$
C) $$\frac{12}{15}$$= $$\frac{12*14}{15*14}$$= $$\frac{166}{210}$$
D) $$\frac{17}{21}$$ = $$\frac{17*10}{21*10}$$ = $$\frac{170}{210}$$
E) $$\frac{29}{35}$$ = $$\frac{29*6}{35*6}$$= $$\frac{174}{210}$$

We see that A is the largest.
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Which of the following fractions is the largest? [#permalink]

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30 Oct 2017, 08:48
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Bunuel wrote:
Which of the following fractions is the largest?

A. 5/6

B. 11/14

C. 12/15

D. 17/21

E. 29/35

hi..

the fractions are such that you can do away with LCM and thus some sort of calculations..

Remember - when we add SIMILAR quantity to BOTH numerator and denominator the resulting number is BIGGER
example $$1/2 <\frac{1+1}{2+1}<\frac{1+3}{2+3}$$

now lets see the choices..

Compare B and C as both have a difference of 3 in numerator and denominator.. 11/14 and 12/15 $$\frac{12}{15}= \frac{11+1}{14+1}$$, so 12/15 is bigger
Now $$\frac{5}{6}= \frac{5*3}{6*3}=\frac{15}{18}$$... similarly 15/18>12/15
so A is the greatest in A,B and C..

lets check A with D and E...

D 17/21..... difference of 4 in numerator and denominator, so multiply 5/6 with 4/4.... $$\frac{5*4}{6*4}=\frac{20}{24}=\frac{17+3}{21+3}>\frac{17}{21}$$.... so A is greater

compare with E.
E 29/35...... $$\frac{5}{6} = \frac{30}{36}=\frac{29+1}{35+1}>\frac{29}{35}$$
so A is greater

ans A
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Re: Which of the following fractions is the largest? [#permalink]

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01 Nov 2017, 06:35
Check the difference between the numerator and denominator.

Fraction with least difference with be the highest fraction.
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Re: Which of the following fractions is the largest? [#permalink]

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01 Nov 2017, 07:36
nehasri wrote:
Check the difference between the numerator and denominator.

Fraction with least difference with be the highest fraction.

Hi nehasri,

This logic will not be useful when the difference between numerator and denominator will be the same for different fractions
E.g. 1/2 & 2/3

In this question also if option E had been 30/35 which is 6/7 then the approach would have to be changed

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Re: Which of the following fractions is the largest?   [#permalink] 01 Nov 2017, 07:36
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