Chapter 1.4, Problem 2STP

For Exercises $1-5,$ choose the correct letter.

Which pair of expressions are equivalent?

F. $18m\cdot 0$ and 1

H. $(12-5)+\pi$ and $7\pi$

G. $6+r+11$ and $6\cdot r\cdot 11$

I. $x(3-3)$ and 0

To determine

To choose: The pair of expression that is equivalent to each other.

Explanation of Solution

Given information:

The expressions are $18m\cdot 0\text{ and }1$ , $\left(12-5\right)+\pi \text{ and 7}\pi$ , $6+r+11\text{ and 6}\cdot \text{r}\cdot \text{11}$ and $x\left(3-3\right)\text{ and 0}$ .

The first pair of expression $18m\cdot 0\text{ and }1$ can be solved as follows:

$18m\cdot 0=0\left[0\cdot a=0\right]$

It can be seen that the pair of expression $18m\cdot 0\text{ and }1$ are not equivalent since $0\ne 1$ .

The second pair of expression $\left(12-5\right)+\pi \text{ and 7}\pi$ can be solved as follows:

$\left(12-5\right)+\pi =7+\pi$

It can be seen that the pair of expression $\left(12-5\right)+\pi \text{ and 7}\pi$ are not equivalent since $7+\pi \ne 7\pi$ .

The third pair of expression $6+r+11\text{ and 6}\cdot \text{r}\cdot \text{11}$ can be solved as follows:

$\begin{array}{l}6+r+11=17+r\\ \text{ and }\\ \text{6}\cdot \text{r}\cdot \text{11}=66r\end{array}$

It can be seen that the pair of expression $6+r+11\text{ and 6}\cdot \text{r}\cdot \text{11}$ are not equivalent since $17+r\ne 66r$ .

The fourth pair of expression $6+r+11\text{ and 6}\cdot \text{r}\cdot \text{11}$ can be solved as follows:

$\begin{array}{c}x\left(3-3\right)=x\cdot 0\left[\because x\cdot 0=0\right]\\ =0\end{array}$

It can be seen that the pair of expression $6+r+11\text{ and 6}\cdot \text{r}\cdot \text{11}$ is equivalent.

Therefore, it can be seen from all the answers that the last option $6+r+11\text{ and 6}\cdot \text{r}\cdot \text{11}$ is correct.