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How to divide Monomials?

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  • Last Updated : 31 May, 2022

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) = x2-1 

= 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)

= 2a

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

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