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)
+3
−4
−5
−3
+2
+4
Explanation
(a) Start with 10 positive tokens, remove 7 positive tokens, 3 positive tokens remain. (b) Start with 8 negative tokens, remove 4 negative tokens, 4 negative tokens remain. (c) Start with 9 negative tokens, remove 4 negative tokens, 5 negative tokens remain. (d) Start with 9 positive tokens, need to remove 12. Add 3 zero pairs, then remove 12 positive tokens, leaving 3 negative tokens. (e) Start with 5 negative tokens, need to remove 7 negative. Add 2 zero pairs, then remove 7 negative tokens, leaving 2 positive tokens. (f) Start with 2 negative tokens, need to remove 6 negative. Add 4 zero pairs, then remove 6 negative tokens, leaving 4 positive tokens.