Comparing and Ordering Numbers

Learning Objectives

Use <, >, and = symbols correctly
Order sets of numbers from least to greatest and greatest to least

Concept Explanation

Comparing numbers means determining which number is greater than, less than, or equal to another number. We use the symbols > (greater than), < (less than), and = (equal to) to show these relationships. When comparing multi-digit numbers, we start by comparing the digits in the highest place value position.

Ordering numbers involves arranging them in sequence, either from smallest to largest (ascending order) or largest to smallest (descending order).

Worked Examples

Example 1

Problem: Compare 45 and 54 using the correct symbol.
Solution: 45 < 54
Explanation: Both numbers have the same digits, but in 54, the 5 is in the tens place, making it larger than 45.

Example 2

Problem: Order these numbers from least to greatest: 37, 73, 33, 77
Solution: 33, 37, 73, 77
Explanation: Compare the tens place first, then the ones place to determine the order.

Example 3

Problem: Which symbol makes this statement true? 82 ___ 28
Solution: 82 > 28
Explanation: 82 has 8 tens and 2 ones, while 28 has 2 tens and 8 ones. Since 8 tens is more than 2 tens, 82 is greater than 28.

Common Errors

Error	Correction	Reason
Confusing the < and > symbols	Remember the symbol points to the smaller number	The wide part of the symbol faces the larger number.
Comparing only the first digit	Compare digits in the same place value	25 is not greater than 19 just because 2 > 1; compare tens to tens.
Ignoring place value	Start comparing from the highest place value	When comparing 352 and 348, look at the hundreds first (3=3), then tens (5>4).

Practice Problems

Problem: Compare 67 and 76 using the correct symbol.

Solution: 67 < 76
Problem: Order from greatest to least: 15, 51, 55, 11

Solution: 55, 51, 15, 11
Problem: Which symbol makes this true? 43 ___ 34

Solution: 43 > 34
Problem: Order from least to greatest: 102, 120, 210, 201

Solution: 102, 120, 201, 210
Problem: Compare 199 and 201 using the correct symbol.

Solution: 199 < 201

Real-World Application Example

Comparing and ordering numbers is essential for many everyday activities, such as finding the best price when shopping, determining which team scored more points in a game, or organizing data in a meaningful way. These skills help us make informed decisions based on numerical information.

Related Concepts

Rounding Numbers (Number Sense & Place Value)
Understanding Place Value (Number Sense & Place Value)
Writing Numbers in Expanded Form (Number Sense & Place Value)