You have to Compare the given fractions in a number of problems in Data Interpretation and Quantitative Ability. Let us study some of the common methods of identifying out the largest or smallest of a given set of fractions which are useful for Mental Maths.
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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