Question

What is the distance between 120 and -130 on a number line?

Answer 1

Answer:

250

Step-by-step explanation:

120 is 120 spaces from zero

-130 is 130 spaces from zero

130+120=250

250 spaces from each other

Answer 2

Answer:

250

Step-by-step explanation:

You can think of this in different ways. Here are two ways.

1) The distance between any two points on the number line is the absolute value of the difference of the coordinates. Since you will take the absolute value of the difference, it makes no different in which order you do the subtraction.

For points on the number line with coordinates a and b,

distance = |a - b| = |b - a|

Here the coordinates are -130 and 120.

distance = |-130 - 120| = |-250| = 250

distance = |120 - (-130)| = |120 + 130| = |250| = 250

As you can see, the distance comes out the same no matter the order of the subtraction.

distance = 250

2) Just think of what the problem means and do a little calculation.

120 is a positive number, so it is located 120 units to the right of zero.

-130 is a negative number, so it is located 130 units to the left of zero.

To find the distance between the two numbers, think of starting at -130. You need to go 130 units right to reach zero. Then from zero you need to move another 120 units right to reach 120. The total distance is 130 + 120 which equals 250.

distance = 250