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nydus/The First Steps in AlgebraPublic

This textbook introduces the fundamental concepts of algebra, including definitions of units, quantities, and number symbols. It explains the use of letters to represent numbers and outlines the signs for basic mathematical operations.

Page 13 of 227
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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