Greater than Less than Lesson

In the place value lesson, we learned about a group of numbers known as the whole numbers. The whole numbers begin with a 0 and increase in increments of 1 indefinitely.
Whole Numbers: {0,1,2,3,4,5,…}
The three dots, known as an ellipsis, indicate our pattern continues forever, after 5 would come 6, then 7, so on and so forth. We can visually show the whole numbers using a number line. Our number line begins with a 0 in the leftmost position. Each additional notch moving right indicates an increase by 1 or the next whole number. No matter how big our number line, we can never show all of the whole numbers. For this reason, we place an arrow at the right end; it indicates that the whole numbers continue forever. There are numbers to the left of 0 and between each whole number. We will talk about those groups of numbers as we get further along. For now, we will focus on only the whole numbers, and keep things very simple.
The number line allows us to visually display two key properties:

• Numbers increase from left to right: →
• Numbers decrease from right to left: ←

Think about the relationship between the numbers 3 and 6, which is larger? Most of you understand 6 is the larger number without using a number line. It's easiest to think about this example using money. If I have $6, I know that I have more than if I only have $3. How can we prove this mathematically? Looking at the number line, we see that 6 lies to the right of 3 on the number line and is, therefore, a larger number. In math, we can place certain symbols between two quantities to show the relationship between the numbers:

• "=" : Equals, the two quantities are equal
• "≠" : Not Equal, the two quantities are not equal
• "<" : Less Than, the left quantity is less than the right quantity
• ">" : Greater Than, the left quantity is greater than the right quantity

Going back to the numbers 6, and 3, we can arrange 6 and 3 in such a way that 3 out of the 4 symbols could be used to describe their relationship to each other.

• 6 ≠ 3 : 6 is not equal to 3
• 6 > 3 : 6 is greater than 3
• 3 < 6 : 3 is less than 6

These symbols can all be confusing at first. When working with the inequality symbols "<" less than and ">" greater than, the trick is to remember the correct symbol will always point to the smaller number. Therefore, if the smaller number is on the left, use a less than "<" symbol. Alternatively, if the larger number is on the right, use a greater than ">" symbol. Let's look at a few examples; you can use the number line as needed.
Example 1: Replace the ? with "<" or ">".
12 ? 18 12 < 18
12 is to the left of 18 on the number line and represents a smaller number. Since 12 is on the left, we use the less than "<" symbol. Remember to always use the inequality symbol that points to the smaller number. If the problem had been reversed as: 18 ? 12, we would have used a greater than ">" symbol. In that case, the larger number 18 is on the left side.
18 > 12
Example 2: Replace the ? with "<" or ">".
21 ? 15 21 > 15
21 is to the right of 15 on the number line and represents a larger number. Since 21 is on the left, we use the greater than ">" symbol. Remember to always use the inequality symbol that points to the smaller number.

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