Question

What is the quotient of \[6\] times a number and \[16\]?

Answer 1

Hint: We are supposed to find the quotient of the number that satisfies the condition. Quotient is nothing but the result after dividing certain numbers. It is also mentioned that ‘times a number’, this means that multiplying a certain number to a certain number is mentioned a number of times.

Complete step-by-step solution:
Now let us start solving the given problem.
Since there is no specified number mentioned, we will be considering it as any variable.
We are supposed to find the quotient so let's name it as \[Q\].
Let us take any variable, say it as \[x\].
Now \[6\] times a number is equal to\[6x\].
Now \[6\] and \[16\] times a number would be \[\dfrac{6x}{16}\].
Since it is mentioned that \[6\] times a number and \[16\], it can either be written as \[\dfrac{6x}{16}\] or \[\dfrac{16}{6x}\].
\[\therefore \]Our required answer is \[Q\]\[=\dfrac{6x}{16}\] or \[Q=\dfrac{16}{6x}\]

Note: Since we have two unknown values with us, we would not be able to solve them and find the values accurately. But we can find it randomly but not accurately by trial and error method just by substituting a random value to one of the variables as shown below.
Consider the equation \[Q=\dfrac{6x}{16}\]
Let us put a value to \[x\] and let that be \[4\].
On substituting and solving
We get,
\[\begin{align}
  & Q=\dfrac{6\left( 4 \right)}{16} \\
 & Q=\dfrac{24}{16} \\
 & Q=\dfrac{3}{2} \\
 & Q=1.5 \\
\end{align}\]
So, on substituting one of the values we get the quotient as \[1.5\].
And this would be our trial and error method.