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, 4x², 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, 15x²y/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) (x²/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. 

(x²/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  4a³ ÷ 2a.

Solution: 

Here 2a and 4a³ are the two monomials

The simplest way to divide an algebraic expression is the cancellation of the common terms, which is similar to the division of the numbers.

4a³ ÷ 2a

= (4 × a × a × a)/ (2 × a)

Now,we have to cancel out the common terms, 

= (4/2 )(a³/a)

= 2a² 

Question 2: Divide 50x² by 5x.

Solution:

Let’s divide 50x² by 5x

Step 1: Divide the coefficients. 

50/5 = 10

Step 2: Here ,cancel the common terms 

x²/x = x

At last what we left after all the steps:

= 10x 

Question 3: Using the dividing monomials rule, Divide 44m³n by 4n.

Solution: 

Given: Monomials are 44m³n 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) (m³) (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.

(m³ )(n/n) = m³

= m³

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

i.e, 11m³

Question 4: Divide 6x²y²z³ by 3x²yz²?

Solution:

Given: Monomials are 6x²y²z³ and 3x²yz²

Now to Divide: 6x²y²z³ by 3x²yz²

Step 1: Separately consider the coefficients and variables.

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

= (6/3) (x² /x²) (y²/y) (z³/z²)

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.

= (x² /x²) (y²/y) (z³/z²)

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 64xy² by -4xy?

Solution: 

Given: 64xy² and -4xy 

Now, to divide 64xy² by -4xy

If we simplify separately all the constant and variables, 

= -(64/4)(x/x) (y²/y)

= -4y

Question 6: Divide 56xy³z⁴ by 7xy³z²?

Solution:

Given: Monomials are 56xy³z⁴ and 7xy³z².

Now to Divide: 56xy³z⁴ by 7xy³z²

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) (y³/y³) (z⁴/z²)

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 ) (y³/y³) ( z⁴/z² )

After simplifying, we will get

= z²

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

i.e, 8z²