Question
Answers

Fill in the blanks: $\dfrac{5}{{12}} \div (.............) = - \dfrac{{35}}{{18}}$
1) $ - \dfrac{{21}}{{36}}$ 2) $ - \dfrac{{12}}{{19}}$ 3)$ - \dfrac{5}{{18}}$ 4)$ - \dfrac{3}{{14}}$

Answer
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Hint: We will use operations on fractions to find the value of the missing fractions. So we will assume the unknown fraction to be ‘x’ and solve the given fraction equation to find the value of ‘x’.
Complete step-by-step answer:
According to the question we need to find the missing fraction in the equation: $\dfrac{5}{{12}} \div (.............) = - \dfrac{{35}}{{18}}$
Let the missing fraction be ‘x’.
Then the equation with ‘x’ will now change to:
$\dfrac{5}{{12}} \div x = - \dfrac{{35}}{{18}}$
The operation on the left between two fractions is division. So to solve for x, we will take the reciprocal of x on the LHS and division will become multiplication. So it will become:
$\dfrac{5}{{12}} \times \dfrac{1}{x} = - \dfrac{{35}}{{18}}$
Solving further, by taking $\dfrac{5}{{12}}$ to the other side, it will become the reciprocal $\dfrac{{12}}{5}$ , the equation will change to:
$ \dfrac{1}{x} = - \dfrac{{35}}{{18}} \times \dfrac{{12}}{5} \\
   \Rightarrow \dfrac{1}{x} = - \dfrac{{7 \times 2}}{3} \\
   \Rightarrow \dfrac{1}{x} = - \dfrac{{14}}{3} \\ $
Now, we will take the reciprocal and get the value of ‘x’ as
$x = - \dfrac{3}{{14}}$
 Hence, the correct answer is option D.

Note: In this question, we were required to take the reciprocal of the unknown fraction . We should be careful that for division of fractions, we need to take the reciprocal of the fraction and then use the multiplication operation on the fraction. And if there is a whole number then we need to take its reciprocal and multiply the reciprocal. For example, if we have to calculate $\dfrac{2}{3} \div 4$ , then we will take the reciprocal of 4 and change the sign of division with multiplication, to get $\dfrac{2}{3} \times \dfrac{1}{4}$ , and then solve and simplify to get the answer as : $\dfrac{1}{6}$ .