Division of Monomials

Division of monomials means product of their quotient of numerical coefficients and quotient of their literal coefficients.


Since, the product of 3m and 5n = 3m × 5n = 15mn; it follows that

(i) \(\frac{15mn}{3m} = \frac{3   \times   5   \times   m   \times   n}{3   \times   m}\) = 5n

or, 15mn ÷ 3m = 5n

i.e. when 15mn is divided by 3m, the quotient is 5n.

(ii) \(\frac{15mn}{5n} = \frac{3   \times   5   \times   m   \times   n}{5   \times   n}\) = 3m

or, 15mn ÷ 5n = 3m

i.e. when 15mn is divided by 5n, the quotient is 3m.

1. Divide 35mxy by 5my

35mxy ÷ 5my

= \(\frac{35mxy}{5my}\)

Now, we need to write each term in the expanded form and then cancel the terms which are common to both numerator and denominator.

= \(\frac{\not{5}   \times   7   \times   \not{m}   \times   x  \times   \not{y}}{\not{5}   \times   \not{m}   \times   \not{y}}\)

= 7x


2. Divide 14a7 by 2a5

14a7 ÷ 2a5

= \(\frac{14a^{7}}{2a^{5}}\)

Now, we need to write each term in the expanded form and then cancel the terms which are common to both numerator and denominator.

= \(\frac{\not{2}   \times   7   \times   \not{a}   \times   \not{a}   \times   \not{a}   \times   \not{a}   \times   \not{a}   \times   a   \times   a}{\not{2}   \times   \not{a}   \times   \not{a}   \times   \not{a}   \times   \not{a}   \times   \not{a}}\)

= 7 × a × a

= 7a2

Or, we can solve this in the other way.

14a7 ÷ 2a5

= \(\frac{14a^{7}}{2a^{5}}\)

= \(\frac{14}{2} \times \frac{a^{7}}{a^{5}}\)

Now we will write the each numerical part \((\frac{14}{2})\) in the expanded form and then cancel the terms which are common to both numerator and denominator and in case of literal part subtract the smaller power of a literal from bigger power of the same literal.

= \(\frac{\not{2} \times 7}{\not{2}} \times a^{7 - 5}\)

= 7 × 2

= 7a2



3. Divide the monomial: 81p3q6 by 27p6q3

81p3q6 ÷ 27p6q3

= \(\frac{81p^{3}q^{6}}{27p^{6}q^{3}}\)

= \(\frac{81}{27} \times \frac{p^{3}q^{6}}{p^{6}q^{3}}\)

Now we will write the each numerical part (\frac{81}{27}) in the expanded form and then cancel the terms which are common to both numerator and denominator and in case of literal part subtract the smaller power of a literal from bigger power of the same literal.

= \(\frac{\not{3}   \times   \not{3}   \times   \not{3}   \times   3}{\not{3}   \times   \not{3}   \times   \not{3}}   \times   \frac{q^{6   -   3}}{p^{6   -   3}}\)

= \(3 \times \frac{q^{3}}{p^{3}}\)

= \(\frac{3q^{3}}{p^{3}}\)

Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials






Algebra Page

6th Grade Page

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