# Roots and Powers of Algebraic Expressions

### Greater Than Symbol in Math: Examples & Problems

This lesson explains what the 'greater than' symbol is and how to use it to compare numbers in mathematics. You'll learn when to use the 'greater than' symbol how to tell the difference between the 'greater than' and 'less than' symbols, then you'll be quizzed about what you've learned.

### The Greater Than Symbol and Its Meaning

When you compare pieces of data in mathematics, not everything is equivalent. Sometimes you find or are looking for a range of values that satisfy a certain condition. This range of values can show up in three main ways:
1. They can be greater than a certain number
2. Less than a certain number
3. Between two numbers

When this happens, we use symbols to illustrate how we are comparing the numbers we are working with, whether individual numbers or variables. The greater than symbol is written as >. The greater than symbol shows that one or more numbers are larger or 'greater' than a given value. We'll explain this in more detail shortly.

The less than symbol is written as <. The less than symbol shows that one or more numbers are smaller or 'less' than a given value.

### Telling Greater Than from Less Than

Now that you've seen the greater than > and less than < symbols, you can see they look similar to each other. In fact, they're mirror opposites of each other. So how can we tell the difference between the two symbols?

Compare the V-like shape of the symbols to the mouth of an alligator. Remember that the alligator always wants to eat as much as it can, so it opens its jaws to the larger quantity.

Also remember that most of us naturally read from left to right, so if the open end of the mouth comes first, >, we have the greater than sign. For example, 3 > 1. We know that 3 is indeed larger than 1, so we write our symbol with the open end pointing at the three. We read the statement as '3 is greater than 1.'

Now consider this statement: 1 < 3. Notice how the order of the numbers has changed in this example, but the open end of the symbol still faces the larger number. The alligator still wants to eat the 3! How do we read this statement, though? If we read the statement from left to right, we cannot say '3 is greater than 1,' even though it's a true statement. This is because we read the '1' first. In this case, we say that 1 is less than 3. See the difference?

### Lesson Summary

The greater than symbol tells us that the number or variable to the left of the symbol is more, or greater than, the number or variable to the right of the symbol. To understand which symbol to write when comparing two values, think of the hungry alligator. The alligator's mouth always opens towards the larger value so that it can eat as much as possible.

If the mouth opens to the left (>), such as 5 > 4, we read the statement as a greater than. In this case,
we would read it as '5 is greater than 4.'
• If the mouth opens to the right (<), such as 7 < 10, we read the statement as a less than. In this case, we
would read it as '7 is less than 10.'

Notice how the alligator mouth opens to the larger number no matter what!