Q1.
Evaluate these expressions by thinking of them as the resulting movement of combining button presses: a. (+ 1) + (+ 4) b. (+ 4) + (+ 1) c. (+ 4) + (– 3) + (– 2) d. (– 1) + (+ 2) + (– 3)
Answer
Here the numbers are movements, not floors. Add them one after another to get the total movement.
a. (+ 1) + (+ 4) = + 5 → 1 floor up, then 4 more up = 5 floors up
b. (+ 4) + (+ 1) = + 5 → 4 floors up, then 1 more up = 5 floors up
c. (+ 4) + (– 3) + (– 2) = (+ 1) + (– 2) = – 1 → 4 up, 3 down, 2 down = 1 floor down
d. (– 1) + (+ 2) + (– 3) = (+ 1) + (– 3) = – 2 → 1 down, 2 up, 3 down = 2 floors down
b. (+ 4) + (+ 1) = + 5 → 4 floors up, then 1 more up = 5 floors up
c. (+ 4) + (– 3) + (– 2) = (+ 1) + (– 2) = – 1 → 4 up, 3 down, 2 down = 1 floor down
d. (– 1) + (+ 2) + (– 3) = (+ 1) + (– 3) = – 2 → 1 down, 2 up, 3 down = 2 floors down
Why this is the same as before: whether the first number is a floor or a movement, the rule for combining is the same addition. Three separate presses of + 4, – 3 and – 2 have exactly the same effect as one press of – 1.
Tip: To add a long string quickly, total the ‘+’ numbers and the ‘–’ numbers separately. In (c): + 4 against – 3 – 2 = – 5, and 4 – 5 = – 1.