How to Divide Monomials

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The phrase "monomial," as the name implies, is made up of the terms "mono" and "nomial," which relate to a single expression. A monomial is an algebraic or mathematical phrase consisting of just one term with no mathematical operation. Furthermore, the monomial terms can be variables or mixed terms with a co-efficient. Furthermore, the variable's power (let's say \(x\)) in a monomial should be an integer, not a fractional power like the squared or cube root.
For example, \(2x^{\frac{1}{3}}\) is not a monomial as the term has a fraction power of \(x\). Now, monomial is a type of polynomial, about which we will learn next.

Types of Polynomials

Polynomials are classified into three categories based on the number of terms. Monomials, binomials, and trinomials are the three types. Let us go over these in greater detail:

Monomial: They consist of just a single term but there is one condition. The term cannot be zero.
Example: \(6x^2, \ 7x^3, \ 67x\), etc.
Binomial: Binomials consist of just two terms and they must have a mathematical operation in between.
Example: \(6x^2 \ + \ 7x^3, \ 8x^2 \ + \ 7y, \ xy^2 \ + \ 3x\), etc.
Trinomial: Trinomial consist of three terms and between every two terms there is a mathematical operation.
Example: \(2x^2 \ + \ 3x \ + \ 10, \ 4x^3 \ + \ 3x^2 \ + \ 7, \ 3x^2y \ + \ 4xy \ + \ 6\), etc.

Degree of a Monomial Expression

Follow these procedures to determine the degree of a single variable expression:

The degree of a monomial would be the highest power of \(x\). That’s it!

Example: \(4x^3\) has the degree \(3\) since the exponent of \(x\) is \(3\).
Example: \(3x^2y^3\) has the degree \(5\) since the term has the power of \(x \ = \ 2\) and \(y \ = \ 3\), so the addition comes to \(5\).

Dividing Monomials

To divide monomials, follow these steps:

While dividing monomials, we must divide separately the coefficients and the variables.
Next, for exponent values with the same base, we must subtract the exponents.
Then, simplify the expression.

Examples:

\(\frac{24x^2 y^3}{6xy} \ = \ 4xy^2\)
\(\frac{18x^5 y^6}{3x^2 y^5} \ = \ 6x^3y\)
\(\frac{12xy^3}{2xy^2} \ = \ 6y\)

Free printable Worksheets

Exercises for Dividing Monomials

1) \( \frac{4x^2y^3z}{4yz} = \)

2) \( \frac{-12x^2y^3z}{2yz} = \)

3) \(6xz^2 \ \div \ 2xz^2 = \)

4) \(-8xz^2 \ \div \ 2xz^2 = \)

5) \(-4x^2y^3 \ \div \ 4y = \)

6) \(-24x^2y^3 \ \div \ 3y = \)

7) \(28x^2y^3 \ \div \ 4y = \)

8) \( \frac{-6xzy}{-3yz} = \)

9) \( \frac{10xzy}{-2yz} = \)

10) \( \frac{12xzy}{-2yz} = \)

Answers

1) \( \frac{4x^2y^3z}{4yz} = \)\( \ \color{red}{x^2y^2}\)

2) \( \frac{-12x^2y^3z}{2yz} = \)\( \ \color{red}{-6x^2y^2}\)

3) \(6xz^2 \ \div \ 2xz^2 = \)\( \ \color{red}{3}\)

4) \(-8xz^2 \ \div \ 2xz^2 = \)\( \ \color{red}{-4}\)

5) \(-4x^2y^3 \ \div \ 4y = \)\( \ \color{red}{-x^2y^2}\)

6) \(-24x^2y^3 \ \div \ 3y = \)\( \ \color{red}{-8x^2y^2}\)

7) \(28x^2y^3 \ \div \ 4y = \)\( \ \color{red}{7x^2y^2}\)

8) \( \frac{-6xzy}{-3yz} = \)\( \ \color{red}{2x}\)

9) \( \frac{10xzy}{-2yz} = \)\( \ \color{red}{-5x}\)

10) \( \frac{12xzy}{-2yz} = \)\( \ \color{red}{-6x}\)

How to Divide Monomials