Removing grouping symbols: Level 2 The relationship of a − b to b − a We know the relationship of a + b to b + a: a + b = b + a. But what is the relationship of a − b to b − a ? a − b is the negative of b − a. a − b = −(b − a). For example, 2 − 5 = −(5 − 2). Problem 20. Prove: a − b = −(b − a). To see the answer, pass your mouse over the colored area.
Solution 2. Two numbers are negatives of one another if their sum is 0.
a − b and b − a clearly satisfy that test: a − b + b − a = 0. Therefore, a − b = −(b − a).
to −1.
We may interpret that rule (Lesson 4) to mean: In any fraction we may change the signs
q − p is the negative of p − q. Problem 22. Apply that rule.
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