Question

By what number should $\dfrac{{ - 44}}{9}$ be divided to get $\dfrac{{ - 11}}{3}$

Answer 1

Hint: We have to find the number which when divides $\dfrac{{ - 44}}{9}$ gives $\dfrac{{ - 11}}{3}$ as a result . We should know about the theory of division of fractions to solve this question . We will also solve this question by using the concept of multiplication of terms having a negative sign . We can solve the question using the division formula . We should know about the properties of signs which we get when two opposite signs are multiplied or the properties of signs when the same signs are multiplied with each other.

Complete step-by-step answer:
Given : $\dfrac{{ - 44}}{9}$ is divided such that it gives $\dfrac{{ - 11}}{3}$
Let us consider that -$\dfrac{{ - 44}}{9}$ is divided by $x$ to give $\dfrac{{ - 11}}{3}$
Now , we can solve the question using simple division
Where ,
$x$ is the divisor , $\dfrac{{ - 44}}{9}$ is the dividend and $\dfrac{{ - 11}}{3}$ is the quotient
We know the formula for division
\[Dividend{\text{ }} = {\text{ }}quotient{\text{ }}*{\text{ }}divisor{\text{ }} + {\text{ }}remainder\]
As from the question we can say that the remainder left after division is zero .
So, remainder \[ = {\text{ }}0\]
Putting the values in the formula , we get
$\dfrac{{ - 44}}{9} = {\text{ }}\dfrac{{ - 11}}{3}{\text{ }} \times {\text{ }}x{\text{ }} + {\text{ }}0$
Further ,
$\dfrac{{ - 44}}{9} = {\text{ }}\dfrac{{ - 11}}{3}{\text{ }} \times {\text{ }}x$
On solving ,
\[x{\text{ }} = {\text{ }}\dfrac{4}{3}\]
Thus the required number is \[\dfrac{4}{3}\]
So, the correct answer is “Option B”.

Note: When a number or a term is divided by another number then it is equivalent to that of the number to the reciprocal of the number by which it was divided .We can consider an example as: If a number is written as $\dfrac{{\dfrac{5}{3}}}{2}$ then it can also be written as \[\dfrac{5}{3}{\text{ }} \times {\text{ }}\dfrac{1}{2}\] . The property of signs for the division of two terms is the same as that for the multiplication of the two terms . We get a negative sign when two terms of opposite signs are divided with each other and get a positive sign when two terms of the same signs are divided with each other .