Positive and negative number word problems, step by step

A negative number is easiest to believe when it is a reading on something: a thermometer, a depth gauge, a balance.

The question

What is the difference between the two elevation readings, in meters?

A hiker was at −19 meters at the trailhead and −14 meters by the second marker.
−14 − (−19)
−14 − (−19) = 5 meters
  1. Read it through once. This one asks for the GAP between two readings, and a gap is a distance — it is never negative, however far below zero either reading is.
  2. Write it as a subtraction, and keep the brackets: −14 − (−19). Taking away a negative moves you UP the scale, which is the one signed rule that does not look like what it does.
  3. That comes to 5 meters. Check the SIGN against the story before you write it down — the number is only half the answer here.

How it works.

  1. 01

    Read it through once. This one asks for the GAP between two readings, and a gap is a distance — it is never negative, however far below zero either reading is.

  2. 02

    Write it as a subtraction, and keep the brackets: −14 − (−19). Taking away a negative moves you UP the scale, which is the one signed rule that does not look like what it does.

  3. 03

    That comes to 5 meters. Check the SIGN against the story before you write it down — the number is only half the answer here.