Question

How do you determine if ${\displaystyle \frac{7}{2}}$ is a monomial?

Answer 1

Hint: We will try to find the rules for a given number to be monomial. The first condition being it cannot be variable. It has to be only one term. There can’t be any negative or fractional exponents. We then break the given term ${\displaystyle \frac{7}{2}}$ in decimal and mixed fraction to point out that ${\displaystyle \frac{7}{2}}$ is a monomial.

Complete step by step answer:
A monomial by definition contains just one term. A monomial is the product of non-negative integer powers of variables. Consequently, a monomial has no variable in its denominator. It can only contain one single term. There can’t be any negative or fractional exponents.

Terms can be separated by different basic binary operations of ‘plus’ or ‘minus’.
For our given number ${\displaystyle \frac{7}{2}}$, if we convert it into fraction, we get ${\displaystyle \frac{7}{2}}=3.5$.
This number has an exact position in between 3 and 4. The middle point of 3 and 4 represents the term ${\displaystyle \frac{7}{2}}=3.5$. We can also represent it as a product of non-negative integer power where ${\displaystyle \frac{7}{2}}{x}^0$.

The power or indices being 0, it satisfies all the requirements. Neither the number itself nor its denominator and numerator parts are variable. This all means that any number that isn’t attached to a variable is a monomial.
Therefore, ${\displaystyle \frac{7}{2}}$ is a monomial.

Note: There can be a confusion about the mixed fraction where we break it as ${\displaystyle \frac{7}{2}}=3+{\displaystyle \frac{1}{2}}$. We cannot consider this as two terms. We can overcome this as ${\displaystyle \frac{7}{2}}=(3+{\displaystyle \frac{1}{2}})$. The brackets confirm it being one term. Same rule applies for the fraction part.