Dividing Expressions

Task goals

• Simplify direct quotients by dividing the coefficients and cancelling matching factors, such as $\frac{24x^3y}{6xy}=4x^2$.
• Use the quotient law for the same non-zero base, for example $\frac{a^m}{a^n}=a^{m-n}$ and $\frac{x^5}{x^2}=x^3$.
• Keep signed and multi-variable quotients organised, including forms such as $\frac{30a^2b^3}{5ab}=6ab^2$ and $\frac{-24x^4}{6x}=-4x^3$.
• Use simplified quotients in context, such as finding a missing length from an area expression, and explain why factors may cancel but sums may not.