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nydus/The First Steps in AlgebraPublic
Page 13 of 226
Table of Contents

PARENTHESES.

The second process is represented by 10−(3+2).

If a man has 10 dollars consisting of 2 five-dollar bills, and has a debt of 3 dollars to pay, he can pay his debt by giving a five-dollar bill and receiving 2 dollars.

This process is represented by 10−5+2.

Since the debt paid is 3 dollars, that is, (5−2) dollars, the number of dollars he has left can evidently be expressed by

From (3) and (4) it follows that

If an expression within a parenthesis is preceded by the sign −, the parenthesis can be removed, provided the sign before each term within the parenthesis is changed, the sign + to −, and the sign − to +.

Any part of an expression can be enclosed within a parenthesis and the sign − prefixed, provided the sign of each term enclosed is changed, the sign + to −, and the sign − to +.

Exercise 1.

Remove the parentheses, and combine:

  1. 9+(3+2).
  1. 9+(3−2).
  1. 7+(5+1).
  1. 7+(5−1).
  1. 6+(4+3).
  1. 6+(4−3).
  1. 3+(8−2).
  1. 9−(8−6).
  1. 10−(9−5).
  1. 9−(6+1).
  1. 8−(3+2).
  1. 7−(3−2).
  1. 9−(4+3).
  1. 9−(4−3).
  1. 7−(5−2).
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