Chapter 1.3, Problem 27PPS

To determine

To evaluate the expression:

  $1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}$ , and to name the property used.

Answer to Problem 27PPS

  $1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}=136$

And the property used is associative property of addition.

Explanation of Solution

Given:

  $1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}$

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

  $1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}$

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,

  $\begin{array}{c}1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}=\frac{11}{6}\cdot 24\cdot \frac{34}{11}\\ =\left(\frac{11}{6}\cdot 24\right)\cdot \frac{34}{11}\\ =\left(11\cdot 4\right)\cdot \frac{34}{11}\\ =44\cdot \frac{34}{11}\\ =4\cdot 34\\ =136\end{array}$

Thus,

  $1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}=136$

And the property used is associative property of multiplication.