Division of Algebraic Terms
A mathematical operation of dividing an algebraic term by another algebraic term is called the division of algebraic terms.
Introduction
In algebra, two algebraic terms are connected by the division sign ($\div$) to obtain the quotient of them. There are two cases of dividing the algebraic terms because of the classification of the algebraic terms. It is very important to learn both of the cases to divide any algebraic term by another term.
Required knowledge
For dividing the algebraic terms, learn the following two mathematical concepts firstly.
Now, let us start learning the different cases for dividing the algebraic terms in algebra.
Dividing the Like Terms
Two like algebraic terms are involved in division but the quotient of them is a rational number due to their similarity. Actually, the like algebraic terms have the same literal coefficient and it is a main cause for the disappearance of the literal coefficient in the quotient of them.
Examples
$(1) \,\,\,$ $\dfrac{4a}{2a} \,=\, 2$
$(2) \,\,\,$ $\dfrac{-3g^2}{7g^2} \,=\, -\dfrac{3}{7}$
$(3) \,\,\,$ $\dfrac{2x^2yz^2}{8x^2yz^2} \,=\, \dfrac{1}{4}$
Dividing the Unlike Terms
Similarly, two unlike algebraic terms are also involved in the mathematical operation division but the quotient of them is an algebraic term because of their dissimilarity. In fact, the unlike algebraic terms have different literal coefficients and it makes the division of any two unlike algebraic terms to form another algebraic term as their quotient.
Examples
$(1) \,\,\,$ $\dfrac{6a}{2b} \,=\, \dfrac{3a}{b}$
$(2) \,\,\,$ $\dfrac{g^2}{6h^2} \,=\, \dfrac{g^2}{6h^2}$
$(3) \,\,\,$ $\dfrac{-14xy^2z}{7xyz^2} \,=\, -\dfrac{2y}{z}$