Question

Write the given phrase as an algebraic expression: the quotient of $18\,\,{\text{and}}\,\,n.$

Answer 1

Algebraic expressions are expressions which are made up of variables and constants along with mathematical algebraic operations which are addition, subtraction, multiplication, division etc.
Also Quotient is the term given to the expression which is obtained by dividing one term or number over another term or number or simply quotient is the result of the process of division.
So by using the above two standard definitions we can solve the question given.

Complete step by step solution:
Given statement:
The quotient of $18\,\,{\text{and}}\,\,n....................................\left( i \right)$
Now we know that in mathematics the algebraic expressions are those expressions which are made up of variables and constants along with mathematical algebraic operations which are addition, subtraction, multiplication, division etc.
Algebraic expressions are widely useful and popular since it represents the value of an expression for all of the values a variable can take on.
Now according to the basic definition of a quotient it is a number or a term obtained by dividing one term or number over another term or number.
So according to the definition the mathematical process involved is division and is represented by:
${\text{Quotient = }}\dfrac{x}{y}..............................\left( {ii} \right)$
Also here:

$$x = {\text{Divisor}} \\\ y = {\text{Dividend}} \\\$$

Now on observing the given statement (i): The quotient of $18\,\,{\text{and}}\,\,n$, we can say that here the divisor is $18$ and the dividend is $n.$
Such that on comparison with (ii) we can write:
$\Rightarrow \dfrac{x}{y} = \dfrac{{18}}{n}....................................\left( {iii} \right)$
Therefore the algebraic expression for the phrase the quotient of
$18\,\,{\text{and}}\,\,n$is$\dfrac{{18}}{n}$.

Note: While writing an algebraic expression some of the commonly used words and their corresponding mathematical operations are given below:
1. Addition : plus, sum, more than
2. Subtraction : subtracted, minus, less than, decreased by
3. Multiplication : times, product
4. Division : divided, quotient
Also while making an algebraic expression one must take care that the words and the operations used are mathematically correct or not.