Question

Find 5 rational numbers between 3/4 & 4/5​

Answer 1

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Answer 2

Given: Two rational numbers $\frac{3}{4}$ and $\frac{4}{5}$

To find: 5 rational numbers the given numbers

Solution: The given rational numbers have different denominators. Forst we need to make their denominators same.

LCM of denominators 4 and 5 = 20

To convert these rational numbers with same denominators, we have

$\frac{3}{4} = \frac{3}{4}$ × $\frac{5}{5} = \frac{15}{20}$ and $\frac{4}{5} = \frac{4}{5}$ × $\frac{4}{4} = \frac{16}{20}$

To insert 5 rational numbers, multiply both numerator and denominator of each rational number by 5 + 1 i.e., 6

We have, $\frac{15}{20} = \frac{15}{20}$ × $\frac{6}{6} = \frac{90}{120}$ and $\frac{16}{20} = \frac{16}{20}$ × $\frac{6}{6} = \frac{96}{120}$

Now, we know that 91, 92, 93, 94 and 95 are five integers between 90 and 96.

∵ $\frac{90}{120} < \frac{91}{120} < \frac{92}{120} < \frac{93}{120} < \frac{94}{120} < \frac{95}{120} < \frac{96}{120}$

Hence, 5 rational numbers between $\frac{3}{4}$ and $\frac{4}{5}$ are:

$\frac{91}{120}, \frac{92}{120}, \frac{93}{120}, \frac{94}{120} \ and \ \frac{95}{120}$.