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Mathematics

Insert two rational numbers between −13-\dfrac{1}{3} and −12-\dfrac{1}{2} and arrange in ascending order.

Rational Irrational Nos

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Answer

The L.C.M of 2 and 3 is 6.

−13=−1×23×2=−26−12=−1×32×3=−36Since −3<−2,−12<−13-\dfrac{1}{3} = -\dfrac{1 \times 2}{3 \times 2} = -\dfrac{2}{6} \\[0.5em] -\dfrac{1}{2} = -\dfrac{1 \times 3}{2 \times 3} = -\dfrac{3}{6} \\[0.5em] \text{Since } -3 \lt -2, -\dfrac{1}{2} \lt -\dfrac{1}{3}

A rational number between -12\dfrac{1}{2} and -13\dfrac{1}{3}

=−12+(−13)2=−3+(−2)62=−3−262=−512= \dfrac{-\dfrac{1}{2} + \Big(-\dfrac{1}{3}\Big)}{2} \\[0.5em] = \dfrac{\dfrac{-3 + (-2)}{6}}{2} \\[0.5em] = \dfrac{\dfrac{-3 -2}{6}}{2} \\[0.5em] = \bold{-\dfrac{5}{12}} \\[0.5em]

A rational number between -12\dfrac{1}{2} and -512\dfrac{5}{12}

=−12+(−512)2=−6+(−5)122=−6−5122=−1124= \dfrac{-\dfrac{1}{2} + \Big(-\dfrac{5}{12}\Big)}{2} \\[0.5em] = \dfrac{\dfrac{-6 + (-5)}{12}}{2} \\[0.5em] = \dfrac{\dfrac{-6 -5}{12}}{2} \\[0.5em] = \bold{-\dfrac{11}{24}} \\[0.5em]

Numbers in ascending order are:

−12,−1124,−512,−13\bold{-\dfrac{1}{2}}, \bold{-\dfrac{11}{24}}, \bold{-\dfrac{5}{12}}, \bold{-\dfrac{1}{3}}

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