Chapter 6.6, Problem 3MRE

To determine

Simplify: the given expression.

Answer to Problem 3MRE

The simplest form of $\frac{5x^2}{3y^3}÷\frac{10xy}{9}$ is $\frac{3x}{2y^4}$.

Explanation of Solution

Given information:

The expression $\frac{5x^2}{3y^3}÷\frac{10xy}{9}$.

Formula used:

To divide two fraction, the dividend fraction and the reciprocal of divisor fraction is multiplied.

  $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

  $\frac{5x^2}{3y^3}÷\frac{10xy}{9}$

Recall that to divide two fraction, the dividend fraction and the reciprocal of divisor fraction is multiplied.

  $\begin{array}{l}\frac{5x^2}{3y^3}÷\frac{10xy}{9}\\ =\frac{5x^2}{3y^3}\times \frac{9}{10xy}\\ =\frac{5\cdot x\cdot x}{3y^3}\times \frac{3\cdot 3}{5\cdot 2\cdot x\cdot y}\end{array}$

As $x,5$ and $3$ are common in both numerator and denominator, So, these terms will be cancelled out from both side.

  $\begin{array}{l}=\frac{x}{y^3}\times \frac{3}{2\cdot y}\\ =\boxed{\frac{3x}{2y^4}}\end{array}$

The simplest form of $\frac{5x^2}{3y^3}÷\frac{10xy}{9}$ is $\frac{3x}{2y^4}$.