Suppose we want to solve the following subtraction problem:

We can solve this problem using a number line.

To subtract from we break up into its whole number part () and its decimal part () and proceed in two steps.

• First, we subtract the whole number part. We start at on the number line and move places to the left, which brings us to

• Then, we subtract the decimal part. We move the remaining places to the left, leaving us at

Therefore, we conclude that

We can use the same methods that we learned to subtract whole numbers in more complicated situations.

As an example, let's consider the following problem:

We're subtracting a positive decimal from a smaller positive decimal. So the final answer must be negative.

We start by solving the following easier problem, which is to carry out the subtraction in the reverse order:

However, since our final answer must be negative, we conclude that

Now suppose we have the following problem: In this case, we're subtracting a positive decimal from a negative decimal. So the final answer must be negative.

We start by solving the following easier problem, which is to add their absolute values: However, since our final answer must be negative, we conclude that

Remember

• When we subtract a positive number from a smaller positive number, we carry out the subtraction in the reverse order and then make the final answer negative.

• When we subtract a positive number from a negative number, we add their absolute values and then make the final answer negative.