Interpret positive and negative numbers

Positive and negative integers represent quantities relative to zero, such as gains and losses, elevations above and below a reference level, or movement in opposite directions; zero represents the reference point or absence of signed change. A learner interprets sign, magnitude, opposites, and relative order on a horizontal or vertical number line, understanding that a negative value is less than a positive value and is not necessarily “smaller” in absolute size; formal work with arbitrary real numbers and advanced signed-number operations is outside this scope.

Detailed Explanation: Interpret positive and negative numbers

A signed number tells how a quantity is related to a reference point, usually $0$ .

A positive number, such as $+5$ , is above or to the right of $0$ .
A negative number, such as $-3$ , is below or to the left of $0$ .
Zero means the reference point or no signed change.
The magnitude is the distance from $0$ . For example, $\vert -3 \vert =3$ .
Opposites are the same distance from $0$ but on different sides. The opposite of $+5$ is $-5$ .

Worked example

An elevator starts at the ground floor, labeled $0$ . It moves to floor $+5$ , then to floor $-3$ .

1. Interpret each number.

$+5$ means the elevator is $5$ floors above the ground floor.
$-3$ means the elevator is $3$ floors below the ground floor.
$0$ means the elevator is at the ground floor.

2. Find the magnitude of each position.

The magnitude tells how far the elevator is from floor $0$ :

\vert +5 \vert =5 \qquad \text{and} \qquad \vert -3 \vert =3

So, floor $+5$ is $5$ floors from the ground, and floor $-3$ is $3$ floors from the ground.

3. Compare the two positions.

On a number line, numbers farther to the right are greater:

-3 \quad < \quad 0 \quad < \quad +5

Therefore,

-3<+5

Even though $3$ is less than $5$ in magnitude, $-3$ is still less than $+5$ because every negative number is to the left of every positive number on the number line.

Learn by doing: Interpret positive and negative numbers

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Number Line - Single Operation with Negative Integers, Movement Image to Equation

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