Chapter 1.3, Problem 25PPS

To determine

To evaluate the expression:

  $0.2\cdot 4.6\cdot 5$ , and to name the property used.

Answer to Problem 25PPS

  $0.2\cdot 4.6\cdot 5=4$

And the property used is associative property of addition.

Explanation of Solution

Given:

  $0.2\cdot 4.6\cdot 5$

Concept Used:

Associative property of multiplication:

  $a\cdot b\cdot c=a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c$

Calculation:

In order to evaluate the expression

  $0.2\cdot 4.6\cdot 5$

First simplify mixed fraction and then use inverse property of multiplication according to which

  $a\cdot b\cdot c=a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c$

As,

  $\begin{array}{c}0.2\cdot 4.6\cdot 5=\left(0.2\cdot 4\right)\cdot 5\\ =\left(0.8\right)\cdot 5\\ =4.0\\ =4\end{array}$

Thus,

  $0.2\cdot 4.6\cdot 5=4$

And the property used is associative property of multiplication.