Question

The sum of two rational numbers is -7/12 if one of them is 13by 24 find the other​

Answer 1

Answer:

Given x+(13/24)=-(7/12)

So x=-(7/12)-(13/24)

=-(14/24)-(13/24)

=-27/24

=-9/8

So the answer will be-9 by8

Answer 2

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

• Sum of two numbers = $\sf\:\frac{-7}{12}$

• One of the number = $\sf\:\frac{13}{24}$

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

• Other number whose sum with $\sf\:\frac{13}{24}$ gives $\sf\:\frac{-7}{12}$.

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

Here in the question we are given one number as $\sf\:\frac{13}{24}$ and sum of two rational numbers as $\sf\:\frac{-7}{12}$. We are asked to find the other rational number. So for that we would assume the other rational number as x. Doing so we would frame an equation according to the question. Then solving the equation framed we would get the other rational number. Let's begin !

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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 :

$\sf\:Sum\:of\:two\:rational\:numbers\:=\:\frac{-7}{12}$

• Framing an equation

$\sf\implies\:x+\frac{13}{24}\:=\:\frac{-7}{12}$

• LCM of 1 and 24 = 24

$\sf\implies\:\frac{24x+13}{24}\:=\:\frac{-7}{12}$

• Cross multiplying

$\sf\implies\: 12(24x+13) =(-7) \times 24$

$\sf\implies\: 288x+156 =(-168)$

• Transposing +156 to RHS it becomes -156

$\sf\implies\: 288x =(-168)-156$

$\sf\implies\: 288x =(-324)$

• Transposing 288 to other side it goes to the denominator

$\sf\implies\:x =\frac{(-324)}{288}$

• Reducing the fraction to the lower terms

$\sf\implies\:x =\cancel{\frac{(-324)}{288}}$

$\sf\implies\:x =\cancel{\frac{(-162)}{144}}$

$\sf\implies\:x =\cancel{\frac{(-81)}{72}}$

$\small{\underline{\boxed{\mathrm\red{{\mathfrak{\implies\:x\:=\:\frac{(-9)}{8}}}}}}}$ ★

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

We got the other rational number as $\sf\:\frac{-9}{8}$ . So now let's check if it is correct. For that we would substitute the value of x and the value that is given in the question , in the equation that we have framed. Doing so if we get LHS = RHS our answers would be correct. Let's do :D

$\sf\:Equation~framed~:\:x+\frac{13}{24}\:=\:\frac{-7}{12}$

• Substituting the value we got for x

$\sf\implies\:\frac{-9}{8}+\frac{13}{24}\:=\:\frac{-7}{12}$

• LCM of 8 and 24 = 24

$\sf\implies\:\frac{[3 \times (-9)] + (1 \times 13)}{24}\:=\:\frac{-7}{12}$

$\sf\implies\:\frac{-27 + 13}{24}\:=\:\frac{-7}{12}$

$\sf\implies\:\frac{-14}{24}\:=\:\frac{-7}{12}$

$\sf\implies\:\cancel{\frac{-14}{24}}\:=\:\frac{-7}{12}$

$\sf\implies\:\frac{-7}{12}\:=\:\frac{-7}{12}$

$\bf\implies\:LHS\:=\:RHS$

$\bf\color{blue}{Hence~Verified~!!}$

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$\dag\:\underline{\sf So\:the\:other~rational~number\:is\:\frac{-9}{8}}$ .

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!! Hope it helps !!