Chapter 6, Problem 1P

Understand the meaning of signed numbers.

1. (a) Which is smaller, –12 or –14? _____
2. (b) Mark the following points on a number line: $-5\frac{1}{4},+1.0,-0.75+3\frac{1}{2}$. _____
3. (c) Represent a loss of $250 as a signed number. _____

To determine

The smaller number among $-12\text{ and }-14$.

Answer to Problem 1P

The smaller number among $-12\text{ and }-14$ is $\underset{\_}{-14}$.

Explanation of Solution

Draw the number line and plot the numbers $-12\text{ and }-14$ on the line as shown in the figure below.

From the above Figure 1, observe that $-14$ is to the left of $-12$.

So, $-14$ is smaller than $-12$.

Therefore, the smaller number is $\underset{\_}{-14}$.

To determine

To mark: The given numbers on the number line.

Explanation of Solution

The given numbers are $-5\frac{1}{4},+1.0,-0.75,+3\frac{1}{2}$.

Draw the number line and plot the given numbers on the line as shown in the figure below.

From the above Figure 1, observe that the numbers $-5\frac{1}{4},-0.75$ are to the left of 0 and $+1.0,+3\frac{1}{2}$ are to the right of 0.

To determine

The loss of $250 as a signed number.

Answer to Problem 1P

The loss of $250 can be represented as $\underset{\_}{-\$250}$.

Explanation of Solution

The loss is a negative quantity.

So, loss of $250 is represented by placing a negative sign before the number 250.

Therefore, the loss of $250 can be represented as $\underset{\_}{-\$250}$.