Question

Determine whether the given expression is a monomial. Write yes or no.

Explain your reasoning.

$\frac{5c}{d}$

Short answer

No, the expression$\frac{5c}{d}$ is not a monomial.

Step-by-step solution

Step 1. State the concept of ‘monomial’.

A monomial is a type of polynomial, which is an algebraic expression having only a non-zero single term. Monomial consists of only a single term which makes it easy to do the operation of addition, subtraction and multiplication. It consists of either only one variable or one coefficient or product of a variable and a coefficient with exponents as whole numbers, which represent only one term, unlike binomial and trinomial, which consist of two and three terms respectively. It cannot have a variable in the denominator.

Step 2. State the parts of monomial expression.

The different parts present in the monomial expression are:

Variable: The letters present in the monomial expression.

Coefficient:The number which is multiplied by the variable in the expression.

Degree:The sum of the exponents present in the expression.

Literal part:The alphabets which are present along with the exponent value in the expression.

Example:$4x{y}^2$ is a monomial expression.

Here,the coefficient is 4.

Variables are x and y.

The degree of the monomial expression$=1+2=3$

The literal part is $x{y}^2$.

Step 3. State the conclusion.

From the definition, a monomial expression must contain only one non-zero term.

The expression$\frac{5c}{d}$contains a variable d in the denominator. By the definition of monomial, there must not be any variable in the denominator. The variable in the denominator will be considered as a second term.

Therefore$\frac{5c}{d}$has two terms.

Hence, $\frac{5c}{d}$is not a monomial expression.