Question

find two rational number between 4/5 and 7/13​

Answer 1

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Answer 2

Given: Two rational numbers-  $\frac{4}{5}$ and $\frac{7}{13}$

To find: Two rational numbers between the given numbers

Solution:

The given rational numbers have different denominators. First we need to make their denominators same.

LCM of their denominators 5 and 13 = 65

To convert the rational numbers with same denominators, we have

$\frac{4}{5} = \frac{4}{5}$ × $\frac{13}{13} = \frac{52}{65}$ and $\frac{7}{13} = \frac{7}{13}$ × $\frac{5}{5} = \frac{35}{65}$

We see that 36, 37, 38 ... 50, 51 are integers between 35 and 52.

i.e., $\frac{35}{65} < \frac{36}{65} < \frac{37}{65} \ ... < \frac{50}{65} < \frac{51}{65} < \frac{52}{65}$

Hence, two rational numbers between $\frac{4}{5} \ and \ \frac{7}{13}$ are:

$\frac{36}{65} \ and \ \frac{37}{65}$