Question

Fill in
the blanks
(-2/11) + (-17/3) = (17/5 _
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Answer 1

➤ Correct Question :-

${\bf \leadsto \dfrac{(-2)}{11} + \dfrac{(-17)}{3} = \dfrac{17}{5} + x}$

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★ How to do :-

Here, we are given with two fractions in which we are asked to find a fraction for other fraction which adds up to the same LHS. Then, we shift thr values on the LHS to RHS or RHS to LHS if required, we also verify the statement by checking wether the answer obtained to us is correct or not. Here, we shift the numbers from one hand side to the other, which change it's sign. If the verification says that the LHS is same as RHS, then our answer is corrected. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{(-2)}{11} + \dfrac{(-17)}{3} = \dfrac{17}{5} + x}$

Add the values on LHS.

${\tt \leadsto \dfrac{(-2)}{11} + \dfrac{(-17)}{3}}$

LCM of 11 and 3 is 33.

${\tt \leadsto \dfrac{(-2) \times 3}{11 \times 3} + \dfrac{(-17) \times 11}{3 \times 11}}$

Multiply the numbers on numerator and denominator of both fractions.

${\tt \leadsto \dfrac{(-6)}{33} + \dfrac{(-187)}{33} = \dfrac{(-6) + (-187)}{33}}$

Add the values now.

${\tt \leadsto \dfrac{(-6) - 187}{33} = \dfrac{(-193)}{33}}$

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${\tt \leadsto \dfrac{(-193)}{33} = \dfrac{17}{5} + x}$

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

${\tt \leadsto x = \dfrac{(-193)}{33} - \dfrac{17}{5}}$

LCM of 33 and 5 is 165.

${\tt \leadsto x = \dfrac{(-195) \times 5}{33 \times 5} - \dfrac{17 \times 33}{5 \times 33}}$

Multiply the numerator and denominator of both fractions on RHS.

${\tt \leadsto x = \dfrac{(-975)}{165} - \dfrac{561}{165}}$

Subtract the values now.

${\tt \leadsto x = \dfrac{(-975) - 561}{165} = \dfrac{(-1536)}{165}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{(-512)}{165} = \dfrac{(-512)}{55}}$

Write it as a mixed fraction.

${\tt \leadsto \dfrac{(-512)}{55} = - 9 \dfrac{26}{55}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: is \: \: \: - 9 \dfrac{26}{55}}}}}$