# How do you write the algebraic expression given "the quotient of 14 and the difference between a number and -7"?

Aug 2, 2017

See a solution process below:

#### Explanation:

"the quotient" means to divide.

"the quotient of 14" means 14 is going to be divided by something. So we can write:

$14 \div$

The something it will be divided by is "the difference between a number and -7".

Lets call "a number" $n$.

"the difference" means we are going to subtract something from $n$ and what we are going to subtract is a $- 7$. We can write this as:

$n - \left(- 7\right)$

Putting this together gives:

$14 \div \left(n - \left(- 7\right)\right)$

Or

$\frac{14}{n - \left(- 7\right)}$

Aug 2, 2017

$\frac{14}{\left\mid n + 7 \right\mid}$

#### Explanation:

The "quotient" just means the result of division.

I've interpreted the question with the following qualifications:

• "the quotient of ... and the difference...# means "the quotient of ... divided by the difference (as opposed to the quotient when the difference of ... is divided by 14)
• "the difference between a number and -7" means the absolute difference (it could mean the difference of a number minus -7; or the difference of a number subtracted from -7)

If we represent "a number" by the variable $n$
this gives us the answer shown above.