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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