# How to divide Monomials?

A monomial is a form of a polynomial with a single non-zero term. Because a monomial has only a single term, it is simple to do addition, subtraction, and multiplication. It is composed of only one variable, one coefficient, or the product of a variable and a coefficient, with exponents as whole numbers representing only one term. Whereas binomial and trinomial are also termed polynomials since they have two and three terms, respectively. The denominator cannot contain a variable. Example: 4xy, 4x^{2}, 6xyz, etc

### Dividing Monomial

Dividing monomials is a method of dividing monomials that involves expanding the terms of the two provided expressions and then canceling out the common ones. Polynomials are divided in the same way that monomials are multiplied. When we multiply two monomials, we multiply the coefficients first, then multiply the variables. Similarly, when dividing monomials, divide the coefficients first, then divide the variables. When there are exponents with the same base, divide by subtracting the exponents according to exponent rules.

**Example: 16mn ÷ 4n **

= (16/4) (m) (n/n)

= 4mn

### How to divide Monomials?

**Solution:**

Dividing monomials means dividing the coefficients of two supplied monomials and the variables individually, then combining them to get the result.

Consider the following example, 15x^{2}y/5x

Step 1:Separately consider the coefficients and variables.

Step 2:Expand each constant and variable in the expression by grouping common bases.(15/5) (x

^{2}/x) (y)

Step 3:We can divide the coefficients normally or cancel out the common component, which is 3, from both the numerator and the denominator.15/5 = 3

Step 4:We can keep the common base and subtract the exponents for the variables, or we can simply cancel out one ‘x’ from both the numerator and the denominator.(x

^{2}/x) = x^{2-1}= x

Step 5:Multiply the coefficients and variables obtained by dividing them in steps 3 and 4.i.e, 3xy

### Sample Questions

**Question 1: Divide 4a ^{3} ÷ 2a.**

**Solution: **

Here 2a and 4a

^{3}are the two monomialsThe simplest way to divide an algebraic expression is the cancellation of the common terms, which is similar to the division of the numbers.

4a

^{3}÷ 2a= (4 × a × a × a)/ (2 × a)

Now,we have to cancel out the common terms,

= (4/2 )(a

^{3}/a)= 2a

^{2 }

**Question 2: Divide 50x ^{2} by 5x.**

**Solution:**

Let’s divide 50x

^{2}by 5xStep 1: Divide the coefficients.

50/5 = 10

Step 2: Here ,cancel the common terms

x

^{2}/x = xAt last what we left after all the steps:

= 10x

**Question 3: Using the dividing monomials rule, Divide 44m ^{3}n by 4n.**

**Solution: **

Given: Monomials are 44m

^{3}n and 4n.Step 1: Separately consider the coefficients and variables.

Step 2: Expand each constant and variable in the expression by grouping common bases.

= (44/4) (m

^{3}) (n/n)Step 3: We can divide the coefficients normally or cancel out the common component from both the numerator and the denominator.

= 44/4 = 11

Step 4: We can keep the common base and subtract the exponents for the variables, or we can simply cancel out one from both the numerator and the denominator.

(m

^{3})(n/n) = m^{3}= m

^{3}Step 5: Multiply the coefficients and variables obtained by dividing them in steps 3 and 4.

i.e, 11m

^{3}

**Question 4: Divide 6x ^{2}y^{2}z^{3} by 3x^{2}yz^{2}?**

**Solution:**

Given: Monomials are 6x

^{2}y^{2}z^{3}and 3x^{2}yz^{2}Now to Divide: 6x

^{2}y^{2}z^{3}by 3x^{2}yz^{2}Step 1: Separately consider the coefficients and variables.

Step 2: Expand each constant and variable in the expression by grouping common bases.

= (6/3) (x

^{2}/x^{2}) (y^{2}/y) (z^{3}/z^{2})Step 3: We can divide the coefficients normally or cancel out the common component from both the numerator and the denominator.

= 6/3 = 2

Step 4: We can keep the common base and subtract the exponents for the variables, or we can simply cancel out one from both the numerator and the denominator.

= (x

^{2}/x^{2}) (y^{2}/y) (z^{3}/z^{2})After simplifying, we will get

= yz

Step 5: Multiply the coefficients and variables obtained by dividing them in steps 3 and 4.

i.e, 2yz

**Question 5: Divide 64xy ^{2} by -4xy?**

**Solution: **

Given: 64xy

^{2}and -4xyNow, to divide 64xy

^{2}by -4xyIf we simplify separately all the constant and variables,

= -(64/4)(x/x) (y

^{2}/y)= -4y

**Question 6: Divide 56xy ^{3}z^{4} by 7xy^{3}z^{2}?**

**Solution:**

Given: Monomials are 56xy

^{3}z^{4}and 7xy^{3}z^{2}.Now to Divide: 56xy

^{3}z^{4}by 7xy^{3}z^{2}Step 1: Separately consider the coefficients and variables.

Step 2: Expand each constant and variable in the expression by grouping common bases.

= (56/7) (x /x) (y

^{3}/y^{3}) (z^{4}/z^{2})Step 3: We can divide the coefficients normally or cancel out the common component from both the numerator and the denominator.

= 56/7 = 8

Step 4: We can keep the common base and subtract the exponents for the variables, or we can simply cancel out one from both the numerator and the denominator.

= (x /x ) (y

^{3}/y^{3}) ( z^{4}/z^{2})After simplifying, we will get

= z

^{2}Step 5: Multiply the coefficients and variables obtained by dividing them in steps 3 and 4.

i.e, 8z

^{2}