Quant quiz(shortcut for fractional problems)

Type – 1
When the numerators are same and the denominators are different, the fraction with the largest denominator
 is the smallest.
Have a look at the following example.
Example : Which of the following fractions is the smallest?
(3/5) , (3/7) , (3/13), (3/8)

Here, 13 is the largest denominator, so, (3/13) is the smallest fraction. 5 is the smallest denominator
, hence (3/5) is the largest fraction.
Here logic is very simple, 
Situation: (i) Assume that you are 5 Children in your family. Your Dad brought an Apple and mom cut it into
 5 pieces and distributed among all the children including you. (1/5)
Situation (ii) : Assume that you are 8 Children in your family. Your Dad brought an Apple and mom cut 
it into 8 pieces and distributed among all the children including you. (1/8)

Type 2 :
When the numerators are different and the denominators are same, the fraction with the largest numerator is
 the largest. Have a look at the following example. 

Example : Which of the following fractions is the smallest?
(7/5) , (9/5), (4/5), (11/5)
As 4 is the smallest numerator, the fraction 4/5 is the smallest.
As 11 is the largest numerator, the fraction 11/5 is the largest.

Here too logic is very simple,
Situation 1 : Assume that you are 4 Children in your family. Your Dad brought 8 Apples and mom distributed
 them among all the children including you. (8/4)
Situation 2 :  Assume that you are 4 Children in your family. Your Dad brought 12 Apples and mom 
distributed them among all the children including you. (12/4)

Type 3
The fraction with the largest numerator and the smallest denominator is the largest.
Example: Which of the following fractions is the largest?
(19/16), (24/11), (17/13), (21/14), (23/15)
Solution : As 24 is the largest numerator and 11 is the smallest denominator, 24/11 is the largest fraction. 

Type 4 : 
When the numerators of two fractions are unequal, we try and equate them by suitably cancelling factors or
 by suitably multiplying the numerators. Thereafter we compare the denominators as in TYPE 1. Have a look at 
the following examples.

Example: Which of  the following fractions is the largest?
(64/328), (28/152), (36/176), (49/196)
Solution : 64/328 = 32/164 = 16/82 = 8/41 this is approximately equal to 1/5

Note : In these type of problems, approximate values will be enough. No need to get EXACT values.
25/152 = 14/76 = 7/38 this is approximately equal to 1/5.5
36/176 = 18/88 = 9/44 this is approximately equal to 1/5
49/196 = 7/28 = ¼
As all the numerators are 1 and the least denominator is 4, the fraction 49/196 is the largest

Example: Which of the following fractions is the largest?
(71/181), (214/519), (429/1141)
Solution : (71/181) = (71 X 6) / (181 X 6) = 426/1086
(214/519) = (214 X 2) / (519 X 2) = 428/1038
The numerators are now all ALMOST equal (426, 428 and 429). The smallest denominator is 1038. 
So, the largest fraction must be 428/1038  that is 214/519 :)

Type 5 : 
For a fraction Less than 1 :
If the difference between the numerator and the denominator is same then the fraction with the larger values 
of numerator and denominator will be the largest. Have a look at the following example.

Example: Which of the following fractions is the largest?
(31/37), (23/29), (17/23), (35/41), (13/19) 
Solutions:  difference between the numerator and the denominator of each fraction is 6.... So the fraction with 
the larger numerals i.e., 35/41 is the greatest and the fraction with smaller numerals i.e., 13/19 is the smallest.

Type 6 :
For a fraction Greater than 1
If the difference between the numerator and denominator is same, then the fraction with the smaller values will
 be the largest.

Example : Which of the following fraction is largest ?
(31/27), (43/39), (57/53), (27/23), (29/25)
Solution : As the difference between the numerator and the denominator is same, the fraction with the smaller
 values i.e., 27/23 is the largest.





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