Rules of Division of Algebraic Expression
1) Any number divided by another number is the same as the first number multiplied by the reciprocal of the second number.
1 x
x ÷ y = x X ---------- = ----------
y y
2) The power of literal divided by another power of the same literal is a power of the literal, the index of which is obtained by subtracting the index of the latter from the index of the former.
aᵐ
aᵐ ÷ aⁿ = ------------ = aᵐ ⁻ ⁿ
aⁿ
3) If two numbers literals or terms have like signs then their quotient will be positive, if they have unlike signs then the quotient will be negative
Example – a) ( + ) ÷ ( + ) = ( + )
b) ( - ) ÷ ( - ) = ( + )
c) ( + ) ÷ ( - ) = ( - )
d) ( - ) ÷ ( + ) = ( - )
Division of a term by a number –
To divide a term by a number, divide the numerical coefficient of the term by the number and write the literals of the term with the quotient
Example –
1) 45 a⁷ ÷ 9 = (45 ÷ 9) a⁷ = 5 a⁷
2) (- 120) y⁴ ÷ 30 = (- 120 ÷ 30 ) y⁴ = - 4 y⁴
3) (- 150) y⁴ ÷ (- 30) = {(-150) ÷ (-30 )} y⁴ = 5 y⁴