Question

4. The sum of two rational numbers is-4/9. If one of them is 13/6, then find the other.
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Answer 1

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Answer 2

$\large\sf\underline{Given\::}$

• Sum of two rational numbers = $\sf\:\frac{-4}{9}$

• One of the number = $\sf\:\frac{13}{6}$

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$\large\sf\underline{To\:find\::}$

• The other rational number = ?

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$\large\sf\underline{Assumption\::}$

• Let the other rational number be x .

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$\large\sf\underline{Solution\::}$

According to the question :

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$\sf\:\frac{13}{6}+x=\frac{-4}{9}$

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• LCM of 6 and 1

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$\sf\leadsto\:\frac{13+6x}{6}=\frac{-4}{9}$

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• Cross multiplying

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$\sf\leadsto\:9(13+6x)=6 \times (-4)$

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• Multiplying the terms

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$\sf\leadsto\:117+54x=-24$

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• Transposing 117 to the other side it becomes -ve

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$\sf\leadsto\:54x=-24 -117$

$\sf\leadsto\:54x=-141$

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• Transposing 54 to the other side it goes to denominator

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$\small{\underline{\boxed{\mathrm\red{\leadsto\:x\:=\:\frac{-141}{54}}}}}$ ★

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$\large\sf\underline{Verifying\::}$

$\sf\:\frac{13}{6}+x=\frac{-4}{9}$

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• Substituting the value of x

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$\sf\to\:\frac{13}{6}+(\frac{-141}{54})=\frac{-4}{9}$

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• LCM of 6 and 54 = 54

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$\sf\to\:\frac{(13 \times 9) +(-141) }{54}=\frac{-4}{9}$

$\sf\to\:\frac{117 -141}{54}=\frac{-4}{9}$

$\sf\to\:\frac{-24}{54}=\frac{-4}{9}$

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• Now Cross multiplying

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$\sf\to\:-24 \times 9= -4 \times 54$

$\sf\to\:\cancel{-}216= \cancel{-}216$

$\sf\to\:216=216$

$\small\fbox\blue{Hence\:Verified}$

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$\dag\:\underline{\sf So\:the\:other\:rational\:number\:is\:\frac{-141}{54}}$ .

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!! Hope it helps !!