Question

By what number should $ - \dfrac{5}{{11}}$ be multiplied to get the product $ - \dfrac{3}{{11}}$?

Answer 1

Hint: To solve this question, we will first assume a variable whose value is to be determined. Let it be x, then we will apply the given condition in the question that x multiplied by the number should give the product using the basic concept of multiplication of two numbers as $x \times y = z$. As we know the values of y and z and so put the values in the above equation and hence the value of x can be calculated.

Complete step-by-step answer:
Given: - As the given numbers are $ - \dfrac{5}{{11}}$ and $ - \dfrac{3}{{11}}$.
So, the multiplication of the given number is given by the equation $x \times y = z$.
The value of y is $ - \dfrac{5}{{11}}$ and the value of z is $ - \dfrac{3}{{11}}$.
Let us assume the number as x. Then according to the given condition in the question, x is a rational number and x multiplied by $ - \dfrac{5}{{11}}$ should give $ - \dfrac{3}{{11}}$. Now, let us write this mathematically, then we will have,
$ \Rightarrow x \times - \dfrac{5}{{11}} = - \dfrac{3}{{11}}$
Multiply both sides by 11, then we will have
$ \Rightarrow x \times - \dfrac{5}{{11}} \times 11 = - \dfrac{3}{{11}} \times 11$
Cancel out the common term,
$ \Rightarrow 5x = 3$
Again dividing both the sides of the above equation by 5, we get,
$\therefore x = \dfrac{3}{5}$

Hence, $\dfrac{3}{5}$ should be multiplied by $ - \dfrac{5}{{11}}$ to get the product $ - \dfrac{3}{{11}}$.

Note: Multiplication is one of the four basic operations of arithmetic which gives the result of combining groups of equal sizes. In other words, multiplication is the repeated addition of a quantity. Multiplication is represented by the signs cross ($ \times $), dot '·'. When we multiply two numbers, the answer we get is called 'product'.