Question

divide the sum of 7/8 and 9/11 by -1/4​

Answer 1

★ How to do :-

Here, we are given with two fractions in which we are asked to find the sum of those and then we should divide the sum of those two numbers by an other rational number given. So, first we should find the sum of the first two fractions and then we can divide the obtained answer with the third number given to us. The concepts used here is to take the LCM which helps us to convert the unlike fractions into like fractions. Using this concept, we can find the answer. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \bigg( \dfrac{7}{8} + \dfrac{9}{11} \bigg) \div \dfrac{(-1)}{4}}$

First we should solve the numbers given in bracket.

LCM of 8 and 11 is 88.

${\tt \leadsto \bigg( \dfrac{7 \times 11}{8 \times 11} + \dfrac{9 \times 8}{11 \times 8} \bigg) \div \dfrac{(-1)}{4}}$

Multiply the numerators and denominators of both fractions in bracket.

${\tt \leadsto \bigg( \dfrac{77}{88} + \dfrac{72}{88} \bigg) \div \dfrac{(-1)}{4}}$

Write both numerators with a common denominator in bracket.

${\tt \leadsto \bigg( \dfrac{77 + 72}{88} \bigg) \div \dfrac{(-1)}{4}}$

Add the numerators now.

${\tt \leadsto \dfrac{149}{88} \div \dfrac{(-1)}{4}}$

Now, take the reciprocal of second fraction and multiply both the fractions.

${\tt \leadsto \dfrac{149}{88} \times \dfrac{4}{(-1)}}$

Write the numerator and denominator in lowest form by cancellation method.

${\tt \leadsto \dfrac{149 \times \cancel{4}}{\cancel{88} \times (-1)} = \dfrac{149 \times 1}{22 \times (-1)}}$

Now multiply the numbers in numerator and denominator.

${\tt \leadsto \dfrac{149}{(-22)}}$

Write the obtained fraction in mixed fraction.

${\tt \leadsto \dfrac{149}{(-22)} = - 6 \dfrac{17}{22}}$

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${\red{\underline{\boxed{\bf So, \: the\: answer \: is \: \: - 6 \dfrac{17}{22}}}}}$