Question

The product of two rational numbers is \[\dfrac{{ - 28}}{{81}}\]. If one of the numbers is \[\dfrac{{14}}{{27}}\]. Find the other.

Answer 1

Hint: We are given that the product of any two numbers is \[\dfrac{{ - 28}}{{81}}\]. We already have one number and we have to find the other number so; we will let the other umber be \[x\]. As the product is given so, we will multiply both the numbers and put it equal to \[\dfrac{{ - 28}}{{81}}\], and with this, we will form an equation and determine the value of \[x\] and get the other number.

Complete step by step answer:

We will first consider the given data that is the product is given for two rational numbers be \[\dfrac{{ - 28}}{{81}}\] and one of the numbers is given as \[\dfrac{{14}}{{27}}\] and we have to find the other number.
So, we will consider the other number be \[x\].
Now, according to the problem, we have that the product of two numbers as \[\dfrac{{ - 28}}{{81}}\].
Thus, we will form an equation by multiplying both the numbers and put it equal to \[\dfrac{{ - 28}}{{81}}\].
Hence, we get,
\[
   \Rightarrow \dfrac{{14}}{{27}} \times x = \dfrac{{ - 28}}{{81}} \\
   \Rightarrow x = \dfrac{{ - 28}}{{81}} \times \dfrac{{27}}{{14}} \\
 \]
Now, we will simplify the above expression and determine the value of \[x\].
Thus, we get,
\[
   \Rightarrow x = \dfrac{{ - 2 \times 3}}{9} \\
   \Rightarrow x = \dfrac{{ - 2}}{3} \\
 \]
Hence, the other number is \[\dfrac{{ - 2}}{3}\].

Note: We have to start the solution by letting the other number be as \[x\]. We can form the equation and then simplify it for the value of \[x\]. While solving we have taken the variable \[x\] on one side and the other terms on the right-hand side of the equation. We can verify the obtained number by multiplying both the numbers and check whether to get the same product or not. while doing the cross multiplication, do it properly.