Let's break down the problem step by step:
### Number Line A: Locating [tex]\( p - q \)[/tex]
1. Identify the values of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]:
- [tex]\( p = 3.6 \)[/tex]
- [tex]\( q = 5.2 \)[/tex]
2. Subtract [tex]\( q \)[/tex] from [tex]\( p \)[/tex]:
- [tex]\( p - q = 3.6 - 5.2 \)[/tex]
3. Compute the difference:
- When you subtract 5.2 from 3.6, you end up with [tex]\( -1.6 \)[/tex].
So, on number line A, [tex]\( p - q \)[/tex] is located at [tex]\( -1.6 \)[/tex].
### Number Line B: Locating [tex]\( p + (-q) \)[/tex]
1. Identify the values of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]:
- [tex]\( p = 3.6 \)[/tex]
- [tex]\( q = 5.2 \)[/tex]
2. Compute [tex]\( -q \)[/tex]:
- Since [tex]\( q = 5.2 \)[/tex], then [tex]\( -q = -5.2 \)[/tex].
3. Add [tex]\( p \)[/tex] and [tex]\( -q \)[/tex]:
- [tex]\( p + (-q) = 3.6 + (-5.2) \)[/tex]
4. Compute the sum:
- When you add [tex]\( 3.6 \)[/tex] and [tex]\( -5.2 \)[/tex], you again get [tex]\( -1.6 \)[/tex].
So, on number line B, [tex]\( p + (-q) \)[/tex] is also located at [tex]\( -1.6 \)[/tex].
In conclusion, for both number line A and number line B, the locations are at [tex]\( -1.6 \)[/tex].
