Chapter 4.3, Problem 1E

a.

To determine

To rewrite: The given expression in words and state whether it is true or false.

Answer to Problem 1E

The given expression in words can be written as:

Two divides eight.

The sentence is true.

Explanation of Solution

Given:

The following expression:

  $2|8$

The given expression can be written in words as:

Two divides eight.

The above sentence is true as $8$ is a multiple of $2$ . Hence when $8$ is divided by $2$ , it does not leave a remainder.

  $2\begin{array}{c}\hfill 4\\ \hfill \overline{)\begin{array}{l}8\\ \underset{\_}{8}\\ 0\end{array}}\end{array}$

b.

To determine

To rewrite: The given expression in words and state whether it is true or false.

Answer to Problem 1E

The given expression in words can be written as:

Four divides four.

The sentence is true.

Explanation of Solution

Given:

The following expression:

  $4|4$

The given expression can be written in words as:

Four divides four.

The above sentence is true as $4$ is a multiple of $4$ . Hence when $4$ is divided by $4$ , it does not leave a remainder.

  $4\begin{array}{c}\hfill 1\\ \hfill \overline{)\begin{array}{l}4\\ \underset{\_}{4}\\ 0\end{array}}\end{array}$

c.

To determine

To rewrite: The given expression in words and state whether it is true or false.

Answer to Problem 1E

The given expression in words can be written as:

Two divides one.

The sentence is false.

Explanation of Solution

Given:

The following expression:

  $2|1$

The given expression can be written in words as:

Two divides one.

The above sentence is false as $1$ is not a multiple of $2$ . Hence when $1$ is divided by $2$ , it leaves a remainder.

  $2\begin{array}{c}\hfill 0\\ \hfill \overline{)\begin{array}{l}1\\ \underset{\_}{0}\\ 1\end{array}}\end{array}$

d.

To determine

To rewrite: The given expression in words and state whether it is true or false.

Answer to Problem 1E

The given expression in words can be written as:

Two divide zero.

The sentence is true.

Explanation of Solution

Given:

The following expression:

  $2|0$

The given expression can be written in words as:

Two divide zero.

The above sentence is true as $0$ is a multiple of $2$ . Hence when $0$ is divided by $2$ , it does not leave a remainder.

  $2\begin{array}{c}\hfill 0\\ \hfill \overline{)\begin{array}{l}0\\ \underset{\_}{0}\\ 0\end{array}}\end{array}$

e.

To determine

To rewrite: The given expression in words and state whether it is true or false.

Answer to Problem 1E

The given expression in words can be written as:

Zero divides three.

The sentence is false.

Explanation of Solution

Given:

The following expression:

  $0|3$

The given expression can be written in words as:

Zero divides three.

The above sentence is false as $3$ is not a multiple of $0$ . When $3$ is divided by $0$ , it yields an infinite result