Question

find two rational number between -2/3 and 1/4

Answer 1

Two rational number between $\bold{-\frac{2}{3} \text { and } \frac{1}{4} \text { are }-\frac{5}{24}, \frac{1}{48}}$

Given:  

The two numbers are $-\frac{2}{3}, \frac{1}{4}$

To find:  

The rational number between two numbers

Solution:

Add the numbers and divide their sum by 2.

(i) First rational number between$\frac{-2}{3}, \frac{1}{4}=\frac{-2}{3}+\frac{1}{4}=\frac{-5}{12}$

Divide by 2 $=\frac{-5}{12} \times \frac{1}{2}=\frac{-5}{24}$

The series becomes, $\frac{-2}{3}, \frac{-5}{24}, \frac{1}{4}$

(ii) Second rational number $=\frac{-5}{24}+\frac{1}{4}=\frac{1}{24}$

Divide by 2 $=\frac{1}{24} \times \frac{1}{2}=\frac{1}{48}$

Hence, $\frac{-5}{24}, \frac{1}{48}$ are the two rational numbers

Answer 2

Answer:

Required two rational numbers between $\frac{-2}{3} \: and \: \frac{1}{4}$ are

$\frac{-1}{12} \: and \: \frac{0}{12}$

Step-by-step explanation:

Given Rational numbers $\frac{-2}{3} \: and \: \frac{1}{4}$

i) $\frac{-2}{3}=\frac{-2\times 4}{3 \times 4}$

= $\frac{-8}{12}$---(1)

ii)$\frac{1}{4}=\frac{1\times 3}{4 \times 3}$

=$\frac{3}{12}$----(2)

Now ,

Required two rational numbers between $\frac{-2}{3} \: and \: \frac{1}{4}$ are

$\frac{-1}{12} \: and \: \frac{0}{12}$

Therefore,

Required two rational numbers between $\frac{-2}{3} \: and \: \frac{1}{4}$ are

$\frac{-1}{12} \: and \: \frac{0}{12}$

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