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

## Dividing Monomials Practice Quiz

### More Polynomials courses

- How to Classify Polynomials
- How to Write Polynomials in Standard Form
- How to Multiply Monomials
- How to Simplify Polynomials
- How to Add and Subtract Polynomials
- How to Multiply a Polynomial and a Monomial
- How to Multiply Binomials
- How to Do Operations with Polynomials
- How to Factor Trinomials
- How to Divide Monomials