Q1.
Complete these expressions. a. (+ 40) + ______ = + 200 b. (+ 40) + ______ = – 200 c. (– 50) + ______ = + 200 d. (– 50) + ______ = – 200 e. (– 200) – (– 40) = ______ f. (+ 200) – (+ 40) = ______ g. (– 200) – (+ 40) = ______ Check your answers by thinking about the movement in the mineshaft.
Answer
In the mine, Starting Level + Movement = Target Level, so the missing movement is always Target Level – Starting Level.
| Question | Journey in the mineshaft | Answer | |
|---|---|---|---|
| a. | (+ 40) + ___ = + 200 | from + 40 m up to + 200 m | + 160 |
| b. | (+ 40) + ___ = – 200 | 40 m down to 0, then 200 m more down | – 240 |
| c. | (– 50) + ___ = + 200 | 50 m up to 0, then 200 m more up | + 250 |
| d. | (– 50) + ___ = – 200 | from – 50 m down to – 200 m | – 150 |
| e. | (– 200) – (– 40) | from – 40 m down to – 200 m | – 160 |
| f. | (+ 200) – (+ 40) | from + 40 m up to + 200 m | + 160 |
| g. | (– 200) – (+ 40) | 40 m down to 0, then 200 m more down | – 240 |
Check (b): (+ 40) + (– 240) = – 200 ✔ Check (c): (– 50) + (+ 250) = + 200 ✔
Notice the pairs: (a) and (f) give the same answer, and (b) and (g) give the same answer. That is because ‘find the missing movement’ and ‘Target – Starting’ are two ways of asking exactly the same question.