Question

How do you translate to an algebraic expression the quotient of x divided by 18?

Answer 1

An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. We know that quotients are the result of division between two numbers..

Complete step-by-step solution:
Given “the quotient of x divided by 18”
First we express “the quotient of x” in algebraic expression.
That is we have,
$\Rightarrow \dfrac{m}{x}$.
Here we don’t know the ‘m’ value. (Because quotients are the result of division between two numbers.)
Now we express “the quotient of x divided by 18”
$\Rightarrow \dfrac{{\left( {\dfrac{m}{x}} \right)}}{2}$
Rearranging this we have,
$\Rightarrow \dfrac{m}{{2 \times x}}$.
This requires an algebraic equation. Because we have a constant ‘2’ and a variable ‘m’ and 2 is a coefficient of ‘x’, as it is a constant value used with the variable term and it is well defined. Also we have algebraic operations division and multiplication.

Note: A variable is a symbol for a number that we don’t know yet. Generally it is represented by alphabetic letters. A number on its own is called a constant. Algebra helps in converting a mathematical statement into an equation. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.