The sum of two rational numbers is −49\dfrac{-4}{9}9−4. If one of them is 136\dfrac{13}{6}613, then find the other.
[Hint: Other rational number = −49−136\dfrac{-4}{9} - \dfrac{13}{6}9−4−613]
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Let the other rational number be xxx.
As the sum of the two rational numbers is −49\dfrac{-4}{9}9−4,
⇒136+x=−49⇒x=−49−136[ LCM of 9 and 6=18]⇒x=(−4)×2−13×318⇒x=−8−3918⇒x=−4718=−21118\Rightarrow \dfrac{13}{6} + x = \dfrac{-4}{9} \\[1em] \Rightarrow x = \dfrac{-4}{9} - \dfrac{13}{6} \\[1em] [\text{ LCM of } 9 \text{ and } 6 = 18] \\[1em] \Rightarrow x = \dfrac{(-4) \times 2 - 13 \times 3}{18} \\[1em] \Rightarrow x = \dfrac{-8 - 39}{18} \\[1em] \Rightarrow x = \dfrac{-47}{18} = -2\dfrac{11}{18}⇒613+x=9−4⇒x=9−4−613[ LCM of 9 and 6=18]⇒x=18(−4)×2−13×3⇒x=18−8−39⇒x=18−47=−21811
Hence, the other rational number is −4718\mathbf{\dfrac{-47}{18}}18−47.
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Subtract:
49\dfrac{4}{9}94 from −78\dfrac{-7}{8}8−7
−116\dfrac{-11}{6}6−11 from 83\dfrac{8}{3}38
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