Question

Express the algebraic expression $\frac{4{\mathrm{x}}^2}{9{\mathrm{y}}^2}÷\frac{2\mathrm{x}}{3\mathrm{y}}$in its lowest form.

Answer 1

To simplify : $\frac{4{\mathrm{x}}^2}{9{\mathrm{y}}^2}÷\frac{2\mathrm{x}}{3\mathrm{y}}$

$\frac{4{\mathrm{x}}^2}{9{\mathrm{y}}^2}÷\frac{2\mathrm{x}}{3\mathrm{y}}=\frac{4{\mathrm{x}}^2}{9{\mathrm{y}}^2}\times \frac{3\mathrm{y}}{2\mathrm{x}}$

$=\frac{2\times \mathrm{x}\times \mathrm{x}}{3\times \mathrm{y}\times \mathrm{y}}\times \frac{1\times \mathrm{y}}{1\times \mathrm{x}}$ ( expanding all the literals)

$=\frac{2\times \mathrm{x}\times 1}{3\times \mathrm{y}\times 1}\times \frac{1\times 1}{1\times 1}$

$=\frac{2\mathrm{x}}{3\mathrm{y}}$

Thus, $\frac{4{\mathrm{x}}^2}{9{\mathrm{y}}^2}÷\frac{2\mathrm{x}}{3\mathrm{y}}$$=\frac{2\mathrm{x}}{3\mathrm{y}}$ Answer