Q1.
Evaluate the following differences using tokens. Check that you get the same result as with other methods you now know: a. (+ 10) – (+ 7) b. (– 8) – (– 4) c. (– 9) – (– 4) d. (+ 9) – (+ 12) e. (– 5) – (– 7) f. (– 2) – (– 6)
Answer
| Expression | What you do with the tokens | Answer | |
|---|---|---|---|
| a. | (+ 10) – (+ 7) | Put 10 green, take away 7 green → 3 green left | + 3 |
| b. | (– 8) – (– 4) | Put 8 red, take away 4 red → 4 red left | – 4 |
| c. | (– 9) – (– 4) | Put 9 red, take away 4 red → 5 red left | – 5 |
| d. | (+ 9) – (+ 12) | Put 9 green; add 3 zero pairs to get 12 green, take them away → 3 red left | – 3 |
| e. | (– 5) – (– 7) | Put 5 red; add 2 zero pairs to get 7 red, take them away → 2 green left | + 2 |
| f. | (– 2) – (– 6) | Put 2 red; add 4 zero pairs to get 6 red, take them away → 4 green left | + 4 |
Check with the ‘add the inverse’ rule:
(– 8) – (– 4) = – 8 + 4 = – 4 ✔ (+ 9) – (+ 12) = 9 + (– 12) = – 3 ✔
(– 5) – (– 7) = – 5 + 7 = + 2 ✔ (– 2) – (– 6) = – 2 + 6 = + 4 ✔
(– 5) – (– 7) = – 5 + 7 = + 2 ✔ (– 2) – (– 6) = – 2 + 6 = + 4 ✔
Why zero pairs are needed in d, e and f: you are asked to take away more tokens than you have. Adding zero pairs does not change the value (each pair is worth 0) but it gives you the tokens you need to remove.