Question

Two numbers, n and p are plotted on the number line shown.

n p
<------|---o--------------|------o----------|------>
-1 0 1
The numbers n-p, n+p, and p-n will be plotted on the number line. Select an expression from each list to make this statement true.
The number with the least value is_____
n-p
n+p
p-n
and the number with the greatest value is_____

Answer 1

The number with the least value is p-n when n > p, and the number with the greatest value is n+p.

Let's analyze the three expressions:

n-p: This expression represents the difference between n and p. Since n and p are plotted on the number line, n-p will always be a negative number, indicating that it lies to the left of both n and p.

n+p: This expression represents the sum of n and p. Since n and p are plotted on the number line, n+p will always be a positive number, indicating that it lies to the right of both n and p.

p-n: This expression represents the difference between p and n. Since n and p are plotted on the number line, p-n will be negative when n > p and positive when n < p.

Therefore, the number with the least value is p-n when n > p, and the number with the greatest value is n+p.