To determine the correct description of the sum [tex]\( p + (-9) \)[/tex] where [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are positive numbers, let's analyze the expression step by step:
1. Initial Expression: We start with the expression [tex]\( p + (-9) \)[/tex].
2. Understanding Addition and Subtraction: Adding a negative number is equivalent to subtracting that number from the initial value. Therefore, [tex]\( p + (-9) \)[/tex] is the same as [tex]\( p - 9 \)[/tex].
3. Determining the Direction: When we subtract a positive number from another positive number, we move in the negative direction on the number line because we are reducing the value.
4. Magnitude of Change: The absolute value of [tex]\(-9\)[/tex] is [tex]\( |9| = 9 \)[/tex]. This tells us the distance by which the initial value [tex]\( p \)[/tex] is reduced.
5. Putting it Together: We started with [tex]\( p \)[/tex] and moved [tex]\( 9 \)[/tex] units in the negative direction.
Thus, the sum [tex]\( p + (-9) \)[/tex] is the number located a distance [tex]\( 9 \)[/tex] (the absolute value of [tex]\(-9\)[/tex]) from [tex]\( p \)[/tex] in the negative direction.
So, the correct description is:
The sum [tex]\( p + (-9) \)[/tex] is the number located a distance [tex]\( |9| \)[/tex] from [tex]\( p \)[/tex] in the negative direction.
Therefore, the correct answer is:
- The sum [tex]\( p + (-9) \)[/tex] is the number located a distance [tex]\( |9| \)[/tex] from [tex]\( p \)[/tex] in the negative direction.
