Chapter 1.4, Problem 59STP

To determine

To evaluate the expression:

  $12\cdot 2\cdot 6\cdot 5$ , and to name the property used.

Answer to Problem 59STP

  $12\cdot 2\cdot 6\cdot 5=720$

And the property used is associative property of addition.

Explanation of Solution

Given:

  $12\cdot 2\cdot 6\cdot 5$

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 $12\cdot 2\cdot 6\cdot 5$

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,

  $\begin{array}{c}12\cdot 2\cdot 6\cdot 5=\left(12\cdot 2\right)\cdot 6\cdot 5\\ =\left(24\right)\cdot 6\cdot 5\\ =\left(24\cdot 6\right)\cdot 5\\ =144\cdot 5\\ =720\end{array}$

Thus,

  $12\cdot 2\cdot 6\cdot 5=720$

And the property used is associative property of multiplication.