Question

Divide the sum of $\frac{-8}{7\\}$ and $\frac{3}{14\\}$ by their difference

Answer 1

★ The required answer is 13/19.

Step-by-step explanation:

Analysis:

‎ ‎ ‎ ‎ ‎ ‎In the question, it has been given that we have to divide the sum of two rational numbers by their difference. The given rational numbers are -8/7 and 3/14.

Solution:

‎ ‎ ‎ ‎ ‎ ‎As per the analysis, the mathematical expression which has to be formed is:

$\: \: \: \: \underline{ \boxed{ \tt{ \bigg( \dfrac{ - 8}{7} + \dfrac{3}{14} \bigg) \div \bigg( \dfrac{ - 8}{7} - \dfrac{3}{14} \bigg) }}}$

First let us sum up the two rational numbers.

$\dashrightarrow{\sf{ \dfrac{ - 8}{7} + \dfrac{3}{14} }} \\ \\ \dashrightarrow{ \sf{ \bigg( \dfrac{ - 8}{7} \times \dfrac{2}{2} \bigg) + \bigg( \dfrac{3}{14} \times \dfrac{1}{1} \bigg)}} \\ \\ \dashrightarrow{ \sf{ \bigg( \dfrac{ - 8 \times 2}{14} \bigg) + \bigg( \dfrac{3 \times 1}{14} \bigg) }} \\ \\ \dashrightarrow{ \sf{ \dfrac{ - 16}{14} + \dfrac{3}{14} }} \\ \\ \dashrightarrow{ \sf{ \dfrac{ - 16 + 3}{14} }} \\ \\ \dashrightarrow{ \boxed{ \sf \pmb{ \dfrac{ - 13}{14} }}}$

The sum of two rational numbers is -13/14. Now let's find the difference between the two rational numbers.

$\dashrightarrow{\sf{ \dfrac{ - 8}{7} - \dfrac{3}{14} }} \\ \\ \dashrightarrow{ \sf{ \bigg( \dfrac{ - 8}{7} \times \dfrac{2}{2} \bigg) - \bigg( \dfrac{3}{14} \times \dfrac{1}{1} \bigg)}} \\ \\ \dashrightarrow{ \sf{ \bigg( \dfrac{ - 8 \times 2}{14} \bigg) - \bigg( \dfrac{3 \times 1}{14} \bigg) }} \\ \\ \dashrightarrow{ \sf{ \dfrac{ - 16}{14} - \dfrac{3}{14} }} \\ \\ \dashrightarrow{ \sf{ \dfrac{ - 16 - 3}{14} }} \\ \\ \dashrightarrow{ \boxed{ \sf \pmb{ \dfrac{ - 19}{14} }}}$

We've found the difference too, i.e., -19/14. So, now let's plug in the simplified values in the expression we've formed first.

$\dashrightarrow{\sf { \bigg( \dfrac{ - 8}{7} + \dfrac{3}{14} \bigg) \div \bigg( \dfrac{ - 8}{7} - \dfrac{3}{14} \bigg) }} \\ \\ \dashrightarrow{ \sf{ \dfrac{ - 13}{14} \div \dfrac{ - 19}{14}}} \\ \\ \dashrightarrow{ \sf{ \dfrac{ - 13}{ \cancel{14}} \times \dfrac{ \cancel{14}}{- 19} }} \\ \\ \dashrightarrow{ \sf{ \dfrac{ \cancel- 13}{ \cancel- 19} }} \\ \\ \dashrightarrow \underline{ \boxed{ \frak{ \red{ \pmb{\dfrac{13}{19} }}}}}$

This is the required answer.

• Therefore, the division of sum of the rational numbers -8/7 and 3/14 by the difference of the rational numbers -8/7 and 3/14 is 13/19.

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