# Division of Algebraic Expressions

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In algebra, the division is similar to the division done in arithmetic.

In division of Algebraic-Expressions, we use the laws of exponents.

There are different types of division.

**1) Monomial by monomial.**

2) Polynomial by monomial.

3) Polynomial by binomial.

2) Polynomial by monomial.

3) Polynomial by binomial.

While dividing a monomial by a monomial, we follow the following two rules :

• The coefficients of the quotient of two monomials is equal to the quotient of their coefficients.

• The variable part in the quotient of two monomials is equal to the quotient of the variables in the given monomials.

**Division of a monomial by a monomial**

1) 10x

^{7}÷ 2x

^{4}

**Solution :**

= 10x

^{7}/ 2x

^{4}

= ( 10/2)x

^{7-4}

= 5x

^{3}

2) x

^{4}÷ x

^{4}

**Solution :**

= x

^{4}/ x

^{4}

= x

^{4-4}

= x

^{0}= 1

3) -100a

^{3}÷20a

**Solution :**

= -100a

^{3}/ 20a

= (-100/20)a

^{3-1}

= -5a

^{2}

4) 5m

^{3}÷√5 m

**Solution :**

= 5m

^{3}/√5 m

= (5/√5)m

^{3-1}

=√5m

^{2}

5) Divide 24x

^{2}y

^{2}z

^{2}by 6yz.

**Solution :**

= 24x

^{2}y

^{2}z

^{2}/6yz

= (24/6)x

^{2}y

^{2 -1}z

^{2-1}

= 4x

^{2}yz

_______________________________________________________________

**Practice Problems**

^{6}by x

^{2}monomials. (Ans)

2) Divide by 25y

^{5}by 5y

^{4}monomials. (Ans)

3) Divide by -200x

^{3}by 100x monomials. (Ans)

4)Divide by 25a

^{3}b

^{3}by 5ab monomials. (Ans)

5) Divide by 16 a

^{2}b

^{2}by 4a

^{3}b

^{3}monomials. (Ans)

6) Divide by 30 by 4a

^{3}b

^{3}monomials. (Ans)

**Division of Algebraic Expressions**

• Division of Polynomial by Monomial

• Division of Polynomial by Binomial

• Division of Polynomial by Monomial

• Division of Polynomial by Binomial

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