Question

14. Which of the following fraction is smallest?
14/15
15/19
23/28
21/24​

Answer 1

Answer:

fraction is smallest 21/24 answers

Answer 2

Given: Four fractions $\frac{14}{15}, \frac{15}{19}, \frac{23}{28} \ and \ \frac{21}{24}$

To find: Which of the given fractions is the smallest

Solution:

To compare the given fractions, first we need to make their denominators same so that it becomes easy to compare them using their numerators.

LCM of their denominators 15, 19, 28 and 24 = 15960

⇒ $\frac{14}{15} = \frac{14}{15} \ * \ \frac{1064}{1064} = \frac{14896}{15960}$

⇒ $\frac{15}{19} = \frac{15}{19} \ * \ \frac{840}{840} = \frac{12600}{15960}$

⇒ $\frac{23}{28} = \frac{23}{28} \ * \ \frac{570}{570} = \frac{13110}{15960}$

⇒ $\frac{21}{24} = \frac{21}{24} \ * \ \frac{665}{665} = \frac{13965}{15960}$

On comparing the numerators, we get

12,600 < 13,110 < 13,965 < 14,896

i.e., $\frac{12600}{15960}$ < $\frac{13110}{15960}$ < $\frac{13965}{15960}$ < $\frac{14896}{15960}$

⇒ $\frac{15}{19}$ < $\frac{23}{28}$ < $\frac{21}{24}$ < $\frac{14}{15}$

Hence, the smallest fraction is $\frac{15}{19}$.