Chapter 5.7, Problem 3MRE

To determine

To simplify the given expression.

Answer to Problem 3MRE

  $\frac{8v^2}{15u^2}$

Explanation of Solution

Given:

Expression: $\frac{36u^2}{25v}÷\frac{27u^4}{10v^3}$

Concept used:

To simplify the given expression:

1. Find the Least Common Multiple of the fraction and write in reduced form.
2. Take out common terms in the given expression.
3. Cancel out the terms that are in common in numerator and the denominator.
4. Find if any algebraic identities can simplify the given expression.

Calculation:

Using the above concept,

  $\begin{array}{l}\Rightarrow \frac{36u^2}{25v}÷\frac{27u^4}{10v^3}\\ \Rightarrow \frac{\frac{36u^2}{25v}}{\frac{27u^4}{10v^3}}\\ \Rightarrow \frac{36u^2\times 10v^3}{25v\times 27u^4}\end{array}$

Take out the common terms in the numerator and denominator.

  $\begin{array}{l}\Rightarrow \frac{36u^2\times 10v^3}{25v\times 27u^4}\\ \Rightarrow \frac{4\times 9u^2\times 2\times 5v^3}{5\times 5v\times 3\times 9u^4}\\ \Rightarrow \frac{4\times \cancel{9}{u}^2\times 2\times \cancel{5}{v}^3}{5\times \cancel{5}v\times 3\times \cancel{9}{u}^4}\\ \Rightarrow \frac{4\times \cancel{u\times u}\times 2\times \cancel{v}\times v\times v}{5\times \cancel{v}\times 3\times \cancel{u\times u}\times u\times u}\\ \Rightarrow \frac{4\times 2\times v\times v}{5\times 3\times u\times u}\\ \Rightarrow \frac{8\times v^2}{15\times u^2}\\ \Rightarrow \frac{8v^2}{15u^2}\end{array}$

Conclusion:

Therefore, the simplified form of the expression is $\frac{8v^2}{15u^2}.$