Question

Insert six rational numbers between (i) -1/4 and -2/5​

Answer 1

Answer:

The rational numbers $\frac{ - 1}{4} \: and \: \frac{ - 2 }{5}$ have different denominators.

Equate the denominators.

$\frac{ - 1}{4} \times \frac{5}{5} = \frac{ - 5}{20}$

$\frac{ - 2}{5} \times \frac{4}{4} = \frac{ - 8}{20}$

So, the rational numbers are $\frac{ - 5}{20} and \: \frac{ - 8}{20}$

6 rational numbers between these two rational numbers cannot be written. So, both the numerator and denominator of the two rational numbers is multiplied by 10.

$\frac{ -5 }{20} \times \frac{10}{10} = \frac{ - 50}{200}$

$\frac{ - 8}{20} \times \frac{10}{10} = \frac{ - 80}{200}$

Thus,

The 6 rational no.s between $\frac{ - 1}{4}$ and $\frac{ - 2}{5} \: are:$

$\frac{ - 51}{200}, \frac{ - 52}{200} , \frac{ - 53}{200} , \frac{ - 54}{200} ,\frac{ - 55}{200}$

Hope this helps.

Answer 2

Solution below :-

Step-by-step explanation:

The rational numbers

$\frac{ - 1}{4} \: and \: \frac{ - 2 }{5}$

have different denominators.

Equate the denominators.

$\frac{ - 1}{4} \times \frac{5}{5} = \frac{ - 5}{20}$

$\frac{ - 2}{5} \times \frac{4}{4} = \frac{ - 8}{20}$

$So, the \: rational \: numbers \: are \: \frac{ - 5}{20} and \: \frac{ - 8}{20}$

6 rational numbers between these two rational numbers cannot be written. So, both the numerator and denominator of the two rational numbers is multiplied by 10.

$\frac{ -5 }{20} \times \frac{10}{10} = \frac{ - 50}{200}$

$\frac{ - 8}{20} \times \frac{10}{10} = \frac{ - 80}{200}$

Thus,

The 6 rational no.s between

$\frac{ - 1}{4} </p><p>and \frac{ - 2}{5} \: are:$

$\frac{ - 51}{200}, \frac{ - 52}{200} , \frac{ - 53}{200} , \frac{ - 54}{200} ,\frac{ - 55}{200}$

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"Hope it will be Helpful"