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Removing grouping symbols:  Level 2

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 The relationship of  ab  to  ba

 rule

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).

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To cover the answer again, click "Refresh" ("Reload").
Do the problem yourself first!

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

Solution 2.   See Lesson 2, Problem 9.
Problem 21.    x − 2
2 − 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   pq
  −2
.
  Answer.     pq
  −2
qp
   2

qp is the negative of pq.

Problem 22.   Apply that rule.

  a)   ab
 −c
 =  ba
  c
  b)   2 − x
 −5
 =  x − 2
   5
  c)   x + yz
     −4
 =  xy + z
     4
    d)   x − 1
    2
 =  x + 1
 −2
 =  x + 1
   2
end

Next Lesson:  Adding like terms


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