We want to determine which number is greater and which number is farther from 0. We will do these things one at a time.
Greater Number
To find which number is greater, we can plot both numbers on the number line. Let's do it!
We can see on the diagram that 4 is farther to the right than - 6. This means that 4 is greater than - 6.
Farther From 0
We want to find which number is farther from 0. Let's recall some facts about the absolute value of a number.
The absolute value of a number is its distance from 0 on the number line.
Since distance is always greater than or equal to 0, the absolute value of any number is greater than or equal to 0.
The absolute value of a non-negative number is equal to the number, while the absolute value of a negative number is equal to its opposite.
Let's consider the distances between different numbers and 0 on the number line.
Now, let's find the absolute value of each of the given numbers.
|4|= 4 |- 6|= 6
We can plot the absolute values on a number line to see the order from least to greatest.
Notice that the number that is the farther to the left is |4|. We can also see on the diagram that |- 6| is farther to the right. In this case, the following inequality holds true.
|- 6|> |4|
This means that - 6 is farther from 0 than 4.
