Chapter 1.5, Problem 38PPE

To determine

To Evaluate: The expression $\frac{1}{4}\cdot 24\cdot \frac{2}{3}$

Answer to Problem 38PPE

  $\frac{1}{4}\cdot 24\cdot \frac{2}{3}=4$

Explanation of Solution

Given information:

The expression $\frac{1}{4}\cdot 24\cdot \frac{2}{3}$

Concept and Formula Used:

  $\text{Multiplicative inverse }a\cdot \frac{1}{a}=1,\text{Multiplicative identity }a\cdot 1=1\cdot a=a$

Associative property of multiplication.

Calculation:

The given expression is

  $\begin{array}{l}\frac{1}{4}\cdot 24\cdot \frac{2}{3}=\frac{1}{4}\cdot 4\cdot 2\cdot 3\cdot \frac{2}{3}\left(\text{Substitution of equality}\right)\\ \frac{1}{4}\cdot 24\cdot \frac{2}{3}=\left(\frac{1}{4}\cdot 4\right)\cdot 2\cdot \left(3\cdot \frac{2}{3}\right)\left(\text{Associative property of multiplication}\right)\\ \frac{1}{4}\cdot 24\cdot \frac{2}{3}=\left(1\right)\cdot 2\cdot \left(1\cdot 2\right)\left(\text{Use Multiplicative inverse }\right)\\ \frac{1}{4}\cdot 24\cdot \frac{2}{3}=2\cdot 2\left(\text{Use Multiplicative identity }\right)\\ \frac{1}{4}\cdot 24\cdot \frac{2}{3}=4\left(\text{Multiply }\right)\end{array}$

Conclusion:

  $\frac{1}{4}\cdot 24\cdot \frac{2}{3}=4$