Chapter 1.3, Problem 24PPS

To determine

To evaluate the expression:

  $2\cdot 8\cdot 10\cdot 2$ , and to name the property used.

Answer to Problem 24PPS

  $2\cdot 8\cdot 10\cdot 2=320$

And the property used is associative property of addition.

Explanation of Solution

Given:

  $2\cdot 8\cdot 10\cdot 2$

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

  $2\cdot 8\cdot 10\cdot 2$

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,

  $\begin{array}{c}2\cdot 8\cdot 10\cdot 2=\left(2\cdot 8\right)\cdot 10\cdot 2\\ =\left(16\right)\cdot 10\cdot 2\\ =\left(16\cdot 10\right)\cdot 2\\ =160\cdot 2\\ =320\end{array}$

Thus,

  $2\cdot 8\cdot 10\cdot 2=320$

And the property used is associative property of multiplication.