Removing grouping symbols:  Level 2

Back to Section 1

We know the relationship of  a + b  to  b + a.  They are equal.

a + b = b + a.

But what is the relationship of  ab  to  ba ?

ab is the negative of ba.

ab  =  −(ba).

For example, 5 − 8 = −(8 − 5).

(Compare Lesson 2.)

Problem 20.   Prove:   ab = −(ba).

Do the problem yourself first!

 Solution 1. a − b = a + (−b) = −b + a = −(b − a).

Solution 2.   See Lesson 2, Problem 9.
 Problem 21. x − 22 − x = −1

 The fraction has the form: a −a , which for all a (except 0) is equal

to −1.

 The rule: −a  b = a −b

We may interpret that rule (Lesson 4) to mean:

In any fraction we may change the signs
in both the numerator and denominator.

 Example.   Apply that rule to p − q  −2 .
 Answer. p − q  −2 = q − p   2

qp is the negative of pq.

Problem 22.   Apply that rule.

 a) a − b −c = b − a  c b) 2 − x −5 = x − 2   5
 c) −x + y − z     −4 = x − y + z     4 d) −x − 1    2 = x + 1 −2 = − x + 1   2

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