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.
In comparison of like fractions here are some rectangular figures.
(i)
In (i) shaded portion represents 2/7
(ii)
In (ii) shaded portion represents 3/7
(iii)
In (iii) shaded portion represents 5/7
It is clear that 2/7 < 3/7 < 5/7
or 5/7 > 3/7 > 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
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
Questions and Answers 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) <
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