Find a rational number between -2 …
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Posted by Sunil Harjai 5 years, 4 months ago
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Sia ? 5 years, 4 months ago
The rational number {tex}\left(\frac{-2}{3}+\frac{1}{4}\right){/tex}{tex}\div{/tex} 2 lies in the middle of the two given rational numbers, that is, {tex}\frac{-2}{3}{/tex} and {tex}\frac{1}{4}{/tex}.
Now, {tex}\left(\frac{-2}{3}+\frac{1}{4}\right){/tex} = {tex}\frac{(-2) \times 4 + 3 \times 1}{12}{/tex} = {tex}\frac{-8+3}{12}{/tex} = {tex}\frac{-5}{12}{/tex}
{tex}\therefore{/tex} {tex}\left(\frac{-2}{3}+\frac{1}{4}\right){/tex} {tex}\div{/tex} 2 = {tex}\frac{-5}{12}{/tex} {tex}\div{/tex} 2 = {tex}\frac{-5}{12}{/tex} {tex}\times{/tex} {tex}\frac{1}{2}{/tex} = {tex}\frac{-5}{24}{/tex}
Thus, the required rational number is {tex}\frac{-5}{24}{/tex}. That is, {tex}\frac{-2}{3}{/tex} < {tex}\frac{-5}{24}{/tex} < {tex}\frac{1}{4}{/tex}.
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