Skill: Interpret gains and losses with integers

Choose a reference point and call it $0$. Then use the sign to show direction:

• A positive integer, such as $+5$, means a gain of $5$.
• A negative integer, such as $-5$, means a loss of $5$.
• $0$ means no change.
• The absolute value, written $\vert n \vert$, tells the amount of the gain or loss. The sign tells its direction.

On a number line, positive numbers are to the right of $0$, and negative numbers are to the left.

Example: In a game, a player’s score changes from the starting score. The record shows a change of $-6$ points. What does this mean?

1. The reference point is the starting score, represented by $0$.
2. The negative sign means the score went down, so it is a loss.
3. The amount of the loss is the absolute value:

$$\vert -6 \vert =6$$

4. Therefore, the player lost $6$ points.
5. On a number line, start at $0$ and move $6$ units left. You land at $-6$.

So, $-6$ represents a loss of $6$ points. The number $+6$ would represent a gain of $6$ points, while $0$ would represent no change.