Question

Q. what should be added to the product of the additive inverse of -6/11 and the multiplicative inverse of -8/13 to get the sum 5/11

Chapter Rational numbers, class 8

Kindly solve the Question properly and correct with workings plz.​

Answer 1

★ How to do :-

Here, we are given with some of the hints in which we are asked to find the value of the second number of the same. We are given with the answer of the addition. But, we aren't given with the second fraction to add with. We are asked to find the value of the second fraction by which the first fraction needs to be added. So, first we should multiply the both numbers to get the first fraction. Then, we shift the values from one hand side to the other which changes it's sign. So, let's solve!!

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➤ Solution :-

Additive inverse of ${\sf \dfrac{-6}{11}}$ is ${\sf \dfrac{6}{11}}$

Multiplicative inverse of ${\sf \dfrac{-8}{13}}$ is ${\sf \dfrac{-13}{8}}$

${\tt \leadsto \bigg( \dfrac{6}{11} \times \dfrac{-13}{8} \bigg) + x = \dfrac{5}{11}}$

First we should solve the bracket to get the value of first fraction.

${\tt \leadsto \bigg( \dfrac{6 \times (-13)}{11 \times 8} \bigg) + x = \dfrac{5}{11}}$

Multiply the numerator and denominator of the fraction.

${\tt \leadsto \dfrac{(-78)}{88} + x = \dfrac{5}{11}}$

Write that fraction in the lowest form.

${\tt \leadsto \dfrac{(-39)}{44} + x = \dfrac{5}{11}}$

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

${\tt \leadsto x = \dfrac{5}{11} - \dfrac{(-39)}{44}}$

LCM of 11 and 44 is 44.

${\tt \leadsto x = \dfrac{5 \times 4}{11 \times 4} - \dfrac{(-39)}{44}}$

Multiply the numerator amd denominator of first fraction.

${\tt \leadsto x = \dfrac{20}{44} - \dfrac{(-39)}{44}}$

Subtract the values to get the answer.

${\tt \leadsto x = \dfrac{20 - (-39)}{44} = \dfrac{59}{44}}$

Write the fraction in the form of mixed fraction.

${\tt \leadsto x = \dfrac{59}{44} = 1 \dfrac{15}{44}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: to \: be \: multiplied \: with \: is \: 1 \dfrac{15}{44}}}}}$