Comparing Two-Digit Numbers (>, <, =) - First Grade Mathematics

As numbers grow bigger, comparing them requires a sharp mathematical eye. When you compare two-digit numbers, you cannot just look at the size of individual digits; you must look at their place values! In this chapter, you will learn the golden rule for comparing any two two-digit numbers, discover the famous comparison symbols (> for greater than, < for less than, and = for equal to), and practice reading comparison statements like a true mathematician.

The Comparison Symbols: >, <, and =

Mathematicians use special shorthand symbols so they do not have to write out the words "greater than," "less than," or "equal to" every time.

The Three Comparison Symbols:

   >   GREATER THAN   (Wide open mouth points to the BIGGER number on the left)
                      Example: 85 > 32 ("85 is greater than 32")

   <   LESS THAN      (Small pointed end points to the SMALLER number on the left)
                      Example: 24 < 61 ("24 is less than 61")

   =   EQUAL TO       (Two balanced parallel lines show both sides are the same)
                      Example: 47 = 47 ("47 is equal to 47")

The Hungry Alligator Analogy

A fun way to remember which way the symbol points is to picture the symbol as the open jaws of a hungry alligator. The alligator always wants to eat the biggest meal, so its wide open mouth always opens toward the larger number! The small, sharp point always pokes the smaller number.

The Hungry Alligator:
       48   >   19            15   <   73
     (mouth eats 48)        (mouth eats 73)

The Golden Rule: Compare the Tens First!

When comparing two-digit numbers, always follow this two-step procedure:

Two-Step Comparison Procedure:

Step 1: Look at the TENS digit first!
        Compare 72 and 49:
        72 has 7 tens.
        49 has 4 tens.
        Since 7 tens > 4 tens, 72 > 49!
        (You don't even need to look at the ones!)

Step 2: If the TENS digits are EQUAL, look at the ONES digit!
        Compare 58 and 53:
        Both have 5 tens (TIE!).
        Now compare the ones: 8 ones vs. 3 ones.
        Since 8 > 3, 58 > 53!

Why Tens Always Beat Ones

One ten is worth more than nine ones combined! A number with more tens will ALWAYS be greater than a number with fewer tens, no matter how big the ones digit is. In 49 vs. 72, 49 has a huge ones digit (9), but 72 has 7 tens, while 49 has only 4 tens. 7 tens beats 4 tens every single time!

Practice Exercises

Exercise 1: Compare the numbers 64 and 39 using the correct symbol (> or <). Explain why you chose that symbol by looking at the tens place.

Exercise 2: Compare the numbers 82 and 87 using the correct symbol (> or <). Explain how you decided which number is greater.

Exercise 3: Write the correct comparison symbol (>, <, or =) in each circle: 35 [ ] 53 70 [ ] 70 91 [ ] 89

Exercise 4: A student wrote: 29 > 41 because 9 is bigger than 1. Did the student compare correctly? Explain the student's mistake.

Solutions and Explanations

Solution to Exercise 1: 64 > 39. Looking at the tens place, 64 has 6 tens and 39 has 3 tens. Since 6 tens is greater than 3 tens, 64 is greater than 39.

Solution to Exercise 2: 82 < 87. Both numbers have 8 tens, so we must compare the ones place. 82 has 2 ones, while 87 has 7 ones. Since 2 ones is less than 7 ones, 82 is less than 87.

Solution to Exercise 3: 35 < 53 (3 tens is less than 5 tens). 70 = 70 (both sides have 7 tens and 0 ones). 91 > 89 (9 tens is greater than 8 tens).

Solution to Exercise 4: The student did not compare correctly. The student made the classic mistake of comparing the ones place before checking the tens place. The number 41 has 4 tens, while 29 has only 2 tens. Since 4 tens is greater than 2 tens, 41 is greater than 29, so the correct statement is 29 < 41.