Comparison of Like Fractions

Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example 713 > 213 because 7 > 2.

1. In comparison of like fractions here are some rectangular figures.

(i)

Comparison of Like Fractions

In (i) shaded portion represents 27

(ii) 

Comparison of Like Fractions

In (ii) shaded portion represents 37


(iii)

Comparison of Like Fractions

In (iii) shaded portion represents 57


It is clear that 27 < 37 < 57

or 57 > 37 > 27


Thus, in like fractions or fractions having same denominator, that fraction is greater which has the greater numerator.

Accordingly, 35 > 25; 25 < 35

1517 > 1017; 1017 < 1517



2. Again, let us consider 25 and 35.

2 by 5

25 represents 2 parts out of 5 equal parts on the strip.

3 by 5

35 represents 3 parts out of 5 equal parts on the strip.

3 > 2

Hence, for any two like fractions, the fraction with the larger numerator is greater than the fraction with smaller numerator.

Comparison of Like Fractions

If there are three or more like fractions, they may be arranged in ascending (increasing) and descending (decreasing) order. The order will be according to the order of the numerators.

(a) Ascending order: 19, 29, 39, 49, 59, 69, 79, 89:

as, 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8


(b) Descending order: 89, 79, 59, 49, 39, 29, 19:

as, 8 > 7 > 5 > 4 > 3 > 2 > 1


Similarly again;

(a) Ascending order: 517, 717, 817, 1117, 1317, 1417, 1617:

as, 5 < 7 < 8 < 11 < 13 < 14 < 16

(b) Descending order: 1617, 1417, 1317, 1117, 817, 717, 517:

as, 16 > 14 > 13 > 11 > 8 > 7 > 5



Comparison of Fractions:

Case I: Fractions with same Denominator:

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

For example,

69 > 49

23 < 53


Comparison of fractions with the same denominator

Observe the following figures.

Comparison of Fractions

In the first figure, 2 parts out of 6 equal parts are shaded.

In the second figure, 3 parts out of 6 equal parts are shaded.

Clearly, shaded parts in the second circle are more than those in the first circle.

Thus, 36 > 26 or 26 < 36

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


1. Compare 25 and 45

Solution:

Consider 25, 45

Since, 4 > 2, hence 45 > 25   or   25 < 45


2. Compare 715 and 815

Solution:

Consider 715, 815

Since, 8 > 7, hence 815 > 715  or  715 < 815


Three or more like fractions can be arranged in ascending or descending order by arranging their numerators in ascending or descending order.

For example, the fractions 811, 711, 1011, 311 can be arranged in the ascending order as  311 < 711 < 811 < 1011


Case II: Fraction with Like Numerators:

The fraction with smaller denominator is greater.

Examples:

                  47 > 410;

                 813 > 817;

                 1833 > 1841 etc.


Similarly, 35 < 34;

              1113 < 1110;

              2542 < 2537 etc.


Worksheet on Comparison of Like Fractions:

1. Compare the given fractions and put the right sign <,> or =.

(i) 74 …… 114

(ii) 813 …… 213

(iii) 524 …… 724


Answers:

1. (i) <

(ii) >

(iii) <


2. Put the appropriate sign >, < or = in the box.

(i) 38 ______ 28

(ii) 117 ______ 137

(iii) 29 ______ 79

(iv) 511 ______ 111


Answers:

2. (i) >

(ii) <

(iii) <

(iv) >

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