Chapter 4, Problem 5CST

To determine

To determine which expression is not in its simplest form

Answer to Problem 5CST

D. $\frac{54}{72}$

Explanation of Solution

Given information:

Expression $\frac{1}{64}$

Formula Used: Exponent Rules

Calculation:

Here, check each given option one by one and simplify it.

1. $\frac{1}{2}$

As $\frac{1}{2}$ cannot be broken down further into its prime factors, hence it is in its simplest form.

2. $\frac{21}{32}$

Let us break the fraction into its factors individually.

This will be evaluated as-

  $\frac{21}{32}=\frac{3\times 7}{2\times 2\times 2\times 2\times 2}$

As visible, the fraction cannot be simplified further, hence it is in its simplest form.

3. $\frac{35}{54}$

Let us break the fraction into its factors individually.

This will be evaluated as-

  $\frac{35}{54}=\frac{7\times 5}{3\times 3\times 3\times 2}$

As visible, the fraction cannot be simplified further, hence it is in its simplest form.

4. $\frac{54}{72}$

Let us break the fraction into its factors individually.

This will be evaluated as-

  $\frac{54}{72}=\frac{3\times 3\times 3\times 2}{2\times 2\times 2\times 3\times 3}$

As visible, $3\times 3\times 2$ is common in both numerator & denominator, so they can be cancelled out to give us.

  $\frac{3}{2\times 2}=\frac{3}{4}$

As the fraction can be simplified further, hence it is not in its simplest form.

Hence D is correct.

Conclusion-

D. $\frac{54}{72}$