4-3 Compare and Order Integers

Property

To compare integers, find their positions on a number line. Numbers increase in value as you move from left to right. The symbol's small end ($<$ or $>$) always points to the smaller number.

Examples

• Since $-1$ is to the right of $-3$, we write $-1 > -3$.
• Since $-5$ is to the left of $2$, we write $-5 < 2$.
• $|-5| > |3|$ because this comparison simplifies to $5 > 3$.

Explanation

The number line doesn't lie! Any number to the right is greater than any number to its left. Think of it like a race: the runner at position $-2$ is ahead of the runner at position $-5$.

Property

On a vertical number line, integers positioned higher are greater than integers positioned lower.
If integer $a$ is above integer $b$ on a vertical number line, then $a > b$.
If integer $a$ is below integer $b$ on a vertical number line, then $a < b$.

Examples

Property

To order multiple integers from least to greatest using a number line:
(1) Draw a horizontal number line with appropriate scale;
(2) Plot each integer as a point on the number line;
(3) Read the integers from left to right to get the order from least to greatest.

Examples

Property

For any number $x$, it is always true that $x \leq |x|$ because absolute value represents the distance from zero on the number line.
When comparing absolute values of different numbers, we are comparing their distances from zero, which may not preserve the original ordering of the numbers.

Examples