Comparison of Fractions having the same Numerator

In comparison of fractions having the same numerator the following rectangular figures having the same lengths are divided in different parts to show different denominators.

(i)

Comparison of Fractions having the same Numerator

Shaded portion = 3/10


(ii)

Comparison of Fractions

Shaded portion = 3/5



(iii)

Comparison of Fractions

Shaded portion = 3/4


3/10 < 3/5 < 3/4 or 3/4 > 3/5 > 3/10


In the fractions having the same numerator, that fraction is greater which has the smaller denominator.

5/11 > 5/17, 5/17 < 5/11, 7/15 > 7/16, 7/16 < 7/15


Again, comparison of fractions with the same numerator

Take two strips of the same length:

Comparison of Fractions with the Same Numerator

The first strip is divided into 5 equal parts and the second is divided into 7 equal parts. In the first strip, out of 5 equal parts 3 parts are shaded and in the second strip, out of 7 equal parts 3 parts are shaded. Clearly, the shaded part in the first strip is more than that in the second strip.

Thus, 3/5 > 3/7

Hence, among two fractions having the same numerator, the fraction with the smaller denominator is greater than the other.


Solved Examples on Comparison of Fractions having the same Numerator:

1. Compare 6/9, 6/11

Solution:

6/9  and  6/11

Since, 9 < 11

Hence, 6/9 > 6/11


1. Compare 12/17, 12/14

Solution:

12/17  and  12/14

Since, 17 > 14

Hence, 12/17 < 12/14


Comparison Fractions with same Numerator

If two fractions have the same numerator, the fraction with the smaller denominator denotes the greater fraction.

For example,

\(\frac{5}{7}\) > \(\frac{5}{13}\)

\(\frac{9}{15}\) < \(\frac{9}{13}\)


If there are three or more fractions having the same numerator, they may be arranged in ascending (increasing) and descending (decreasing) order. The order will be in opposite order of denominators. The bigger denominator will make the smaller fraction.

(a) Ascending order: 1/9, 1/7, 1/5, 1/4, 1/3

as 9 > 7 > 5 > 4 > 3


(b) Descending order: 5/3, 5/6, 5/9, 5/12, 5/18

as 3 < 6 < 9 < 12 < 18


Similarly again;

(a) Ascending order: 7/11, 7/9, 7/6, 7/5, 7/2

as 11 > 9 > 6 > 5 > 2


(b) Descending order: 11/1, 11/5, 11/7, 11/10, 11/15

as 1 < 5 < 7 < 10 < 15


Ordering of fraction and comparing fractions:

We know, a fraction represents an equal part of a whole thing. 

(a)

comparing fractions





A whole cake = 1 cake

We can also write it as 1/1 which means in half the denominator has 1 part and numerator has taken the 1 part.

1/1 = 1.

(b)

comparing fractions





          \(\frac{1}{2}\)



Now the cake has been divided into two half parts and one part has been taken.

We write it as 1/2.

comparing Fraction

              \(\frac{1}{3}\)                          \(\frac{1}{4}\)                         \(\frac{1}{5}\)                         \(\frac{1}{6}\)

Note:

As the number of the denominator is getting bigger, the size of the part taken is getting smaller.

1 > 1/2 > 1/3 > 1/4 > 1/5 > 1/6 …..

When the numerator is 1 in a fraction number, it is called a unit fraction.

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