Question

4. Solve the following.
If the sum of two rational numbers is
$\frac{ - 8}{27}$
and one of them is -5, find the
other.

​

Answer 1

Given :-

• Sum of two rational numbers is -8/27  

• One of them is -5

To Find :-

• The other one

Solution :-

~Here, we’re given the sum of two rational no.s, one of those rational no.s and we need to find the other rational no. Firstly we’ll let the other rational no. as ‘x’ and then form an equation according to the question. After solving that equation we can get the other rational number.

__________

→ Let the other rational no. be ‘x’

__________

Finding the other rational number :-

$\sf \implies x + \bigg\{ \dfrac{-8}{27} \bigg\} = -5$

$\sf \implies x - \dfrac{8}{27} = -5$

$\sf \implies x = -5 + \dfrac{8}{27}$

$\sf \implies x = \dfrac{-135+8}{27}$

$\boxed{\bf{ \bigstar \;\; x = \dfrac{-127}{27} }}$

__________

Hence,  

• The other rational number is -127/27

__________

Verification :-

$\sf \implies \bigg\{ \dfrac{-127}{27} \bigg\} + \bigg\{ \dfrac{-8}{27} \bigg\}$

$\sf \implies \dfrac{-135}{27}$

$\boxed{\bf{ \leadsto 5 }} \;\;\bigstar$  

__________

Answer 2

Question :-

If the sum of two rational numbers is

$\frac{ - 8}{27}$ and one of them is -5, find the other.

Given :-

• Sum of two rational number is $\dfrac{-8}{27}$

• One of them is -5.

To find :-

The other number.

Solution :-

Let the other number be 'x'.

Now, our equation will be

$\implies\rm x + \left( \dfrac{-8}{27}\right) = -5$

$\implies\rm x - \dfrac{-8}{27}= -5$

$\implies\rm x = -5 \dfrac{8}{27}$

$\implies\rm x = \dfrac{-135 + 8}{27}$

$\implies\rm x = \dfrac{-127}{27}$

Therefore,

$\sf The \:other\: no. \: is\: \dfrac{-127}{27}$

Verification :-

$\implies\sf\left(\dfrac{-127}{27}\right)+ \left(\dfrac{-8}{27}\right)$

$\implies\sf\dfrac{-127}{27} \dfrac{-8}{27}$

$\implies\sf\dfrac{-135}{27}$

$\implies\sf\dfrac{-135}{27}$

$\implies\sf\cancel\dfrac{-135}{27}$

$\implies\sf -5$

-5 = -5

Hence verified.