# How do you translate "the quotient of of a number and 6" into a mathematical expression?

Apr 24, 2018

We can form a quotient of 'x' and 6 in two ways:
$\frac{x}{6}$ and $\frac{6}{x}$.
The first expression may be implied in the order of the question, but it is not actually specified in the term 'quotient'.

#### Explanation:

It is important to note that ALL "mathematical equations" START as some word expression. After all, we are just using the math as a tool to solve real-world problems which we express in normal conversation.

The terms and sentence structure set up the equation, just as the parts of a sentence describe a thought.

"Quotient" is the term for a division. In this case, "a number and 6" does not specify which is the dividend (numerator) and which is the divisor (denominator).

"A number" means that we are looking for a general expression instead of a specific numeric solution - any number will do. So, we use the convention of a 'variable' we will designate as 'x'.

Now we can form a quotient of 'x' and 6 in two ways:
$\frac{x}{6}$ and $\frac{6}{x}$