The number line

Turn the infinite lift on its side by 90°, and it becomes a number line! The negative numbers -1, -2, -3, ... lie to the left of 0, and the positive numbers 1, 2, 3, ... to the right. We usually drop the '+' sign and simply write 1, 2, 3.

Instead of riding a lift, imagine walking along the line. Walking to the right is the positive (forward) direction; walking to the left is the negative (backward) direction. From 5 to 9 you walk 4 steps forward, so 5 + 4 = 9, and the matching subtraction is 9 - 5 = 4. The rules are the same as in the lift:

• Starting Number + Movement = Target Number
• Target Number - Starting Number = Movement needed

From 9 to 3 you walk 6 steps backward, a movement of -6. So 9 + (-6) = 3, and 3 - 9 = -6. From 3 to -2 you walk 5 steps backward: 3 + (-5) = -2, and -2 - 3 = -5.

For big numbers, draw an unmarked number line that shows only 0, and imagine where the other numbers are. For 85 + (-60): start at 85, to the right of 0, and move 60 to the left; you stop at 25, still to the right of 0. So 85 + (-60) = 25. For (-100) - (+250), ask: starting at 250, what movement reaches -100? 250 steps back take you to 0, and 100 more take you to -100: 350 steps back. So (-100) - (+250) = -350.