List first five rational numbers between …
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Sia ? 6 years, 5 months ago
Firstly we need to have common denominators in both the rational numbers
Thus we multiply 2 with 6 and 3 with 4 to get the common denominator 12
We have {tex}-\frac{1}{2}=-\frac{1 \times 6}{2 \times 6}=-\frac{6}{12}{/tex}
{tex}\frac{2}{3}=\frac{2 \times 4}{3 \times 4}=\frac{8}{12}{/tex}
Now, we write the rational numbers between{tex}-6\over 12{/tex}and{tex}8\over 12{/tex}
So, {tex}-\frac{6}{12}<-\frac{4}{12}<-\frac{3}{12}<0<\frac{4}{12}<\frac{6}{12}<\frac{8}{12}{/tex}
{tex}\Rightarrow{/tex} {tex}-\frac{1}{2}<-\frac{1}{3}<-\frac{1}{4}<0<\frac{1}{3}<\frac{1}{2}<\frac{2}{3}{/tex}
∴ five rational numbers between {tex}-\frac{1}{2}{/tex}and {tex}\frac{2}{3}{/tex}are {tex}-\frac{1}{3},-\frac{1}{4}, 0, \frac{1}{3}{/tex}and {tex}\frac{1}{2}{/tex}.
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