# How do you write the expression for quotient of 4 and a number x increased by 6?

Jan 12, 2017

Without punctuation, the expression is ambiguous.

The quotient of 4, and a number increased by 6: $\text{ } \frac{4}{x + 6}$

The quotient of 4 and a number, increased by 6: $\text{ } \frac{4}{x} + 6$

#### Explanation:

This is a good example of how a lack of any punctuation make the meaning of the sentence ambiguous:

"Quotient" is the answer to a division.

The following are possible interpretations of the given expression.
Let the number be $x$

The quotient of 4, and $\textcolor{b l u e}{\text{a number increased by 6}}$:$\text{ } \frac{4}{\textcolor{b l u e}{\left(x + 6\right)}}$

The quotient of $\textcolor{red}{\text{4 and a number}}$, increased by 6: $\text{ } \textcolor{red}{\frac{4}{x}} + 6$

It is important to be able to write math which is given in English
in a mathematical form, keeping the meaning exactly the same.