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Comparing values up to 99

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Comparing Two-Digit Numbers Up to 99

This lesson shows how to compare two numbers up to 99 by examining their tens digit first and their ones digit second. Students learn what the greater than, less than, and equal to symbols mean, and practice ordering numbers using place value blocks and a number line.

What Does Comparing Values Up to 99 Mean?

Comparing two-digit numbers means deciding which number is bigger, which is smaller, or whether they are the same. Every number up to 99 is made of a tens digit and a ones digit, and the fastest way to compare two numbers is to look at those digits in order of importance. This idea builds directly on identifying tens and ones and on understanding the place values of digits up to 99.

Step 1: Compare the Tens Digit First

The tens digit tells you how many groups of ten are in a number, so it always matters more than the ones digit. If one number has more tens than the other, it is automatically the greater number, no matter what the ones digits are.

For example, compare 47 and 52. The number 47 has 4 tens, and 52 has 5 tens. Since 5 tens is more than 4 tens, \( 52 \gt 47 \), or written the other way, \( 47 \lt 52 \).

47 4 tens, 7 ones < 52 5 tens, 2 ones More tens means a greater number, so 47 < 52
Comparing tens blocks shows 52 has more tens than 47, so 47 is less than 52.

Step 2: Compare the Ones Digit When the Tens Match

Sometimes both numbers have the same number of tens. When that happens, the tens digit cannot decide the winner, so you move on to the ones digit instead.

Compare 34 and 38. Both numbers have 3 tens, so look at the ones digits: 4 and 8. Since 8 is more than 4, \( 38 \gt 34 \).

If both the tens digit and the ones digit are exactly the same, the two numbers are equal. For instance, \( 65 = 65 \).

Using the Comparison Symbols

Three symbols describe the relationship between two numbers:

  • \( \gt \) means "is greater than," for example \( 61 \gt 58 \).
  • \( \lt \) means "is less than," for example \( 23 \lt 29 \).
  • \( = \) means "is equal to," for example \( 74 = 74 \).

A helpful trick is to picture the symbol as an open mouth that always faces the bigger number, since it wants to "eat" the greater amount.

Comparing With a Number Line

A number line up to 99 gives another way to compare values. Numbers placed farther to the right are always greater than numbers placed farther to the left, since the line counts upward from 0 to 99.

0 99 47 82 82 is farther right, so 82 > 47
On a number line, the number farther to the right is always the greater value.

Worked Example

Compare 76 and 79 using place value.

Step 1: Look at the tens digits. Both numbers have 7 tens, so the tens digits match.

Step 2: Look at the ones digits. 76 has 6 ones and 79 has 9 ones. Since 9 is greater than 6, \( 79 \gt 76 \).

Practicing this two-step check, comparing tens first and ones second, makes comparing any pair of numbers up to 99 quick and reliable. Strengthening skills such as counting the value of a digit up to 99 makes these comparisons even faster, since you can immediately see how many tens and ones each number holds.

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