Question

find five rational numbers between 3 upon 4 and 4 upon 5​

Answer 1

Hey! mate, Here is your answer...

3/4 × 5/5 = 15/20 × 6/6 = 90/120

4/5 × 4/4 = 16/20 × 6/6 = 96/120

Five rational numbers are 91/120, 92/120, 93/120, 94/120, 95/120.

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Answer 2

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

To find: Five 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 4 and 5 = 20

To convert the 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 five rational numbers, we need to multiply both numerator and denominator of each rational number by 5 + 1 i.e., 6

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

We see that 91, 92, 93, 94 and 95 are five integers between 90 and 96.

i.e., $\frac{90}{120} < \frac{91}{120} < \frac{92}{120} < \frac{93}{120} < \frac{94}{120} < \frac{95}{120} < \frac{96}{120}$

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

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