# How do you translate "the quotient of 14 and the difference between a number and -7 into an algebraic statement?

May 24, 2017

$\frac{14}{n - \left(- 7\right)}$ or $\frac{14}{n + 7}$ where $n$ is the number.

#### Explanation:

Let's do semantic analysis! Just kidding.

Let's break this down.
"The quotient of 14 and the difference between a number and -7"
This can be interpreted to be:

"The quotient of 14 and a number $a$"
Where $a$ is the "difference between a number and -7"

So far we have $\frac{14}{a}$

Now, $a$ is the "difference between a number and -7". Let's call this number $n$. $a$ is the difference between $n$ and -7 which is to say:
$a = n - \left(- 7\right)$

Now we have these two statements:
$\frac{14}{a}$
$a = n - \left(- 7\right)$

Let's put $a$ back into its place:
$\frac{14}{a} = \frac{14}{n - \left(- 7\right)}$

Finally, we clear off the double negative and we get this statement:
$\frac{14}{n + 7}$