Question

6. The sum of two rational numbers is -6/19.
If one of them is 8/57,find the other.
it's urgent plz answer​

Answer 1

★ How to do :-

Here, we are given with one of the rational number that should be added to the other number. We are also given with the answer obtained while solving those two rational numbers. But, we are not given with the second number that the first number should be added with. We are asked to find the same. Here, we use the concept of shifting the numbers from one hand side to the other which changes it's sign. We can find the value of other fraction. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{8}{57} + x = \dfrac{(-6)}{19}}$

Shift the fraction on LHS and RHS, changing it's sign.

${\tt \leadsto x = \dfrac{(-6)}{19} - \dfrac{8}{57}}$

LCM of 19 and 57 is 57.

${\tt \leadsto x = \dfrac{(-6) \times 3}{19 \times 3} - \dfrac{8}{57}}$

Multiply the numerator and denominator of first fraction

${\tt \leadsto x = \dfrac{(-18)}{57} - \dfrac{8}{57}}$

Now, write both numerators with a common denominator.

${\tt \leadsto x = \dfrac{(-18) - 8}{57}}$

Subtract bith numerators to get the answer.

${\tt \leadsto x = \dfrac{(-26)}{57}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \: \dfrac{(-26)}{57}}}}}$

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Verification :-

${\tt \leadsto \dfrac{8}{57} + x = \dfrac{(-6)}{19}}$

Substitute the value of x.

${\tt \leadsto \dfrac{8}{57} + \dfrac{(-26)}{57} = \dfrac{(-6)}{19}}$

Write both numerators with a common denominator.

${\tt \leadsto \dfrac{8 + (-26)}{57} = \dfrac{(-6)}{19}}$

Write the second number in numerator with only one sign.

${\tt \leadsto \dfrac{8 - 26}{57} = \dfrac{(-6)}{19}}$

Subtract the values on numerator on LHS.

${\tt \leadsto \dfrac{(-18)}{57} = \dfrac{(-6)}{19}}$

Write the obtained answer in lowest form by cancellation method.

${\tt \leadsto \dfrac{(-6)}{19} = \dfrac{(-6)}{19}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!