Question

the sum of rational numbers is -5 if one of the rational numbers is 1/3, find the other​

Answer 1

Given :

• The sum of rational numbers = -5

•One of the rational number =$\tt{\dfrac{1}{3} }$

To Find :

• The other number (y) =?

Solution :

Let 'x' and 'y' be the rational number

$\\ \bullet \bf \: x = \frac{1}{3}$

$\bullet\bf{y=?}$

According to the given conditions :

$\implies \sf \: x + y = - 5 \\ \\ \\ \bullet \underline{ \bf{ \red{substituting \: given \: values}}} \\ \\ \\ \implies \sf \frac{1}{3} + y = - 5 \\ \\ \\ \implies \sf \: 1 + 3y = - 15 \\ \\ \\ \implies \sf \: 1 + 3y + 15 = 0 \\ \\ \\ \implies \sf \: 3y + 16 = 0 \\ \\ \\ \implies \sf \: 3y = - 16 \\ \\ \\ \implies \boxed{ \bf{y = \frac{ - 16}{3}}}$

The other number will be,

$\implies \boxed{ \sf{y = \frac{ - 16}{3} }}$

Answer 2

Given :-

• Sum of two rational numbers is -5
• One of rational rational number is 1/3

To find :-

Other rational number

SOLUTION:-

Let the other rational number is x So,

$x+\dfrac{1}{3} = -5$

Transpose +1/3 to R.H.S

$x = -\dfrac{1}{3} -5$

Take L.C.M to the denominator

L.C.M of 3,1 is 3

$x=\dfrac{-1}{3} -\dfrac{5}{1}$

$x=\dfrac{-1-5(3)}{3}$

$x=\dfrac{-1-15}{3}$

$x=\dfrac{-16}{3}$

So, the other number is -16/3

VERIFICATION :-

So, the sum of 14/3 and 1/3 should be -5

$\dfrac{-16}{3} +\dfrac{1}{3} =-5$

$\dfrac{-16+1}{3} =5$

$\dfrac{-15}{3} =-5$

$-5=-5$

Hence L.H.S =R.H.S

VERIFIED!