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# Which of the following fractions is the largest?

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

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

A = 4.xx %
B = 23.xx %
C = 2.xx %
D = 23.xx %
E = 1.xx %

Now, check between (B) an (D)

B = 196/840
D = 195/840

So, (D) is the largest fraction...
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Re: Which of the following fractions is the largest? [#permalink]
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stonecold wrote:
Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

We need to determine the largest fraction. Let’s weed out some obvious ones: 1/72 and 1/45 are each smaller than 13/56, and 1/24 is smaller than 7/30.

So we are left with 7/30 and 13/56 as the candidates for the largest fraction.

To compare two positive fractions, we can cross-multiply the numerator of one fraction with the denominator of the other fraction. That is, if a/b > c/d, then ad > bc (and vice versa), provided that a, b, c, and d are all positive.

Here we want to compare 7/30 and 13/56, and we have 7(56) = 392 and 13(30) = 390. Since 392 > 390, 7/30 > 13/56. Therefore, 7/30 is the largest fraction.

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

Which of the following fractions is the largest?
A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

STEP-1:
A. 1/24 = can be rewritten as 5/120
B. 7/30 = can be rewritten as 28/120
So B is bigger

STEP-2:
B. 7/30 = can be rewritten as 21/90
C. 1/45 = can be rewritten as 2/90
So B is bigger

STEP-3:
D. 13/56 = Here I paused and waited to eliminate B or E

STEP-4:
E. 1/72 = can be rewritten as 5/360
B. 7/30 = can be rewritten as 84/360
So B is bigger

STEP-5:
Coming back to Choices D and B
D. 13/56 = can be rewritten as (13*30)/(30*56) = 390/(30*56)
B. 7/30 = can be rewritten as (7*56)/(30*56) = 392/(30*56)
So B is bigger

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

A. 1/24 (1/24*4/4 =4/96)
B. 7/30 (7/30 * 3/3 = 21/90)
C. 1/45 (1/45 * 2/2 = 2/90)
D. 13/56 (13/56*2/2 = 26/112)
E. 1/72
(1/72)

the larger the numerator and smaller the denominator, the larger is the fraction.
as one can see that A, C and E are smallest their denominators are larger and numerator are smallest
among D and B, B is largest as 21 is little less than 26 but 112 is larger than 90.
So its B
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Re: Which of the following fractions is the largest? [#permalink]
Here lets check

1/24, 1/45,1/72 So 1/24 is the greatest of three.

So betweeen 1/24 nearly 4 % is and 7/30 is nearly 22%

So 7/30 is greater of the 4 . Then between 7/30 and 13/56

we can check by cross multiplication
7 * 56 > 13*30

so 7/30 is greatest
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Re: Which of the following fractions is the largest? [#permalink]
stonecold wrote:
Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

This is how I solved

For larger fraction, the numerator should be larger (denominators are same) and/or denominator should be smaller (numerators are same).

So comparing 1/24, 1/45 and 1/72, we ignore 1/45 and 1/72.

Now compare 7/30 = 0.233
and 13/56 = 0.232 therefore eliminate 13/56

now we are left with 1/24 and 7/30
we arlready know 7/30 = 0.233
and 1/24 = 0.04 .

clearly 7/30 is larger therefore the answer is B
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Re: Which of the following fractions is the largest? [#permalink]
stonecold wrote:
Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

1/24= 4% approximately
7/30=50% approximately
1/45= 2% approximately
13/56 = 25% approximately
1/72 is between 1% and 2%

IMO B

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

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

Find LCM of 24, 30, 45, 56 and 72.
LCM is (8 x 9 x 5 x 7).
Multiple this LCM by each of the fractions.
The greatest number after multiplication is the largest fraction.
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Which of the following fractions is the largest? [#permalink]
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stonecold wrote:
Which of the following fractions is the largest?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

I would recommend the following way.

Multiplication is always easier than Division and less error prone.

Where, the numerator is same, the fraction with least denominator will be largest
Out of $$\frac{1}{24},\frac{1}{45},\frac{1}{72}$$,$$\frac{1}{24}$$ is the largest.

Although none fit in directly here but if the denominator is same then the largest numerator will give largest fraction. Of course we are talking of positive fractions here.
In $$\frac{7}{30}$$ and $$\frac{13}{56}$$, cross multiply to get the denominators equal.
$$\frac{7}{30}=\frac{7*56}{30*56}$$ and $$\frac{13}{56}=\frac{13*30}{30*56}$$
Now the denominators are same 30*56, so compare numerator. => 7*56=392 and 13*30=390
Hence $$\frac{7}{30}$$ is the largest of the two.

Compare $$\frac{1}{24}$$ and $$\frac{7}{30}$$
Make numerator same $$\frac{1}{24}=\frac{1*7}{24*7}$$

Now, while comparing the denominator, 30<24*7 and so we can say that $$\frac{7}{30}$$ is largest.

B
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Re: Which of the following fractions is the largest? [#permalink]
Hello
A,C,E are clearly out.
Next step would be to multiply C and D, both by 4, giving us
C) 28/30
D) 52/56
Now notice that after multiplying numerator by 4, Firstly, Option C numerator is 2 numbers away from being equal to the denominator(30) while 52 is 4 numbers away from being equal to the denominator(56). Secondly, the denominator of C is smaller than D.
Therefore we can certainly say that option C > option D
Re: Which of the following fractions is the largest? [#permalink]
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