The sum of two rational numbers is -6. If one of them is −85\dfrac{-8}{5}5−8, find the other.
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Let xxx be the other number. −85+x=−6⇒x=−61−−85\dfrac{-8}{5} + x = -6 \\[1em] \Rightarrow x = \dfrac{-6}{1} - \dfrac{-8}{5}5−8+x=−6⇒x=1−6−5−8
LCM of 1 and 5 is 5
⇒x=−6×51×5−−8×15×1⇒x=−305−−85⇒x=−30−(−8)5⇒x=−30+85⇒x=−225⇒x=−425\Rightarrow x = \dfrac{-6 \times 5}{1 \times 5} - \dfrac{-8 \times 1}{5 \times 1}\\[1em] \Rightarrow x = \dfrac{-30}{5} - \dfrac{-8}{5}\\[1em] \Rightarrow x = \dfrac{-30 - (-8)}{5}\\[1em] \Rightarrow x = \dfrac{-30 + 8}{5}\\[1em] \Rightarrow x = \dfrac{-22}{5}\\[1em] \Rightarrow x = -4\dfrac{2}{5}⇒x=1×5−6×5−5×1−8×1⇒x=5−30−5−8⇒x=5−30−(−8)⇒x=5−30+8⇒x=5−22⇒x=−452
The sum of two rational numbers is -6, if one of them is −85\dfrac{-8}{5}5−8, the other number is −425-4\dfrac{2}{5}−452.
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