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 \(\frac{7}{13}\) > \(\frac{2}{13}\) because 7 > 2.
1. In comparison of like fractions here are some rectangular figures.
(i)
In (i) shaded portion represents \(\frac{2}{7}\)
(ii)
In (ii) shaded portion represents \(\frac{3}{7}\)
(iii)
In (iii) shaded portion represents \(\frac{5}{7}\)
It is clear that \(\frac{2}{7}\) < \(\frac{3}{7}\) < \(\frac{5}{7}\)
or \(\frac{5}{7}\) > \(\frac{3}{7}\) > \(\frac{2}{7}\)
Thus, in like fractions or fractions having same denominator, that fraction is greater which has the greater numerator.
Accordingly, 3/5 > 2/5; 2/5 < 3/5
15/17 > 10/17; 10/17 < 15/17
2. Again, let us
consider \(\frac{2}{5}\) and \(\frac{3}{5}\).
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\(\frac{2}{5}\) represents 2 parts out of 5 equal parts on the strip.
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\(\frac{3}{5}\) represents 3 parts out of 5 equal parts on the strip.
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3 > 2
Hence, for
any two like fractions, the fraction with the larger numerator is greater than
the fraction with smaller numerator.
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: 1/9, 2/9, 3/9, 4/9, 5/9, 7/9, 8/9:
as, 1 < 2 < 3 < 4 < 5 < 7 < 8
(b) Descending order: 8/9, 7/9, 5/9, 4/9, 3/9, 2/9, 1/9:
as, 8 > 7 > 5 > 4 > 3 > 2 > 1
Similarly again;
(a) Ascending order: 5/17, 7/17, 8/17, 11/17, 13/17, 14/17, 16/17:
as, 5 < 7 < 8 < 11 < 13 < 14 < 16
(b) Descending order: 16/17, 14/17, 13/17, 11/17, 8/17, 7/17, 5/17:
as, 16 > 14 > 13 > 11 > 8 > 7 > 5
Comparison of Fractions:
Fractions with same Denominator:
If two fractions have the same denominator, the fraction with greater numerator denotes the greater fraction.
For example,
\(\frac{6}{9}\) > \(\frac{4}{9}\)
\(\frac{2}{3}\) < \(\frac{5}{3}\)
Comparison of fractions with the same denominator
Observe the following figures.
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, \(\frac{3}{6}\) > \(\frac{2}{6}\) or \(\frac{2}{6}\) < \(\frac{3}{6}\)
Hence, among two fractions having the same denominator, the fraction with the greater numerator is greater than the other.
1. Compare 2/5 and 4/5
Solution:
Consider 2/5, 4/5
Since, 4 > 2, hence 4/5 > 2/5 or 2/5 < 4/5
2. Compare 7/15 and 8/15
Solution:
Consider 7/15, 8/15
Since, 8 > 7, hence 8/5 > 7/5 or 7/5 < 8/5
Worksheet on Comparison of Like Fractions:
1. Compare the given fractions and put the right sign <,> or =.
(i) \(\frac{7}{4}\) …… \(\frac{11}{4}\)
(ii) \(\frac{8}{13}\) …… \(\frac{2}{13}\)
(iii) \(\frac{5}{24}\) …… \(\frac{7}{24}\)
Answers:
1. (i) <
(ii) >
(iii) <
2. Put the appropriate sign >, < or = in the box.
(i) \(\frac{3}{8}\) ______ \(\frac{2}{8}\)
(ii) \(\frac{11}{7}\) ______ \(\frac{13}{7}\)
(iii) \(\frac{2}{9}\) ______ \(\frac{7}{9}\)
(iv) \(\frac{5}{11}\) ______ \(\frac{1}{11}\)
Answers:
2. (i) >
(ii) <
(iii) <
(iv) >
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