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