Lesson 9: The Number Line: Ordering and Comparing

New Concept

To compare two numbers is to decide if they are equal ($=$), or if one is greater ($>$) or less ($<$) than the other.

What’s next

This card introduces the core symbols for comparison. You'll soon apply these to worked examples that involve multi-step calculations before you can compare the results.

Property

A number line is a way to show numbers in order. Numbers increase in value as you move to the right and decrease as you move to the left. The numbers we count with (1, 2, 3...) are counting numbers, and when you add zero, they become whole numbers.

Examples

• Arrange from least to greatest: $15, 5, 51 \rightarrow 5, 15, 51$
• Arrange from least to greatest: $101, 110, 100 \rightarrow 100, 101, 110$
• Arrange from least to greatest: $1, 0, \frac{1}{2} \rightarrow 0, \frac{1}{2}, 1$

Explanation

Think of a number line as a perfectly straight road where every number has its own address. As you travel right, the addresses (numbers) get bigger, and as you travel left, they get smaller. This road helps you see exactly where each number lives, making it super easy to tell which number is greater or lesser.

Property

To compare two numbers, we use symbols to show if they are equal (=) or if one is greater (>) or less (<) than the other. The small, pointy end of the symbol always aims at the smaller number.

Examples

• Compare the numbers: $5012 \bigcirc 5102 \rightarrow 5012 < 5102$
• Use symbols to write: One third is less than one half. $\rightarrow \frac{1}{3} < \frac{1}{2}$
• Compare the lengths: $1 \text{ foot} \bigcirc 10 \text{ inches} \rightarrow 1 \text{ foot} > 10 \text{ inches}$

Explanation

Imagine the > and < symbols are a hungry alligator's mouth! The alligator always wants to eat the bigger meal, so its mouth opens toward the larger number. If both numbers are the same, the alligator gets confused and shuts its mouth, forming an equal sign. It’s a foolproof way to remember your comparison symbols!