Using tokens, argue out the following statements: (a) 7 − 18 = 7 + (−18) (additive inverse of 18 is −18) (b) 4 − (−12) = 4 + 12 (additive inverse of −12 is 12)
Using tokens: Start with 7 positives. Add 11 zero pairs to get 18 positives and 11 negatives. Remove 18 positives. Result: 11 negatives = −11. Similarly, 7 + (−18) = −11. Both methods give the same result.
Using tokens: Start with 4 positives. To remove 12 negatives (which don't exist), add 12 zero pairs. Remove 12 negatives. Result: 16 positives = 16. Similarly, 4 + 12 = 16. Both methods give the same result.
Explanation
(a) The chapter shows that subtracting 18 from 7 requires adding zero pairs since we don't have enough positives to remove. The result is −11, which matches adding −18 to 7. (b) The chapter demonstrates that subtracting a negative number is equivalent to adding its positive counterpart. The token model shows this by adding zero pairs and removing negatives.