Algebra Know-It-ALL

Chapter 4

1. The first sum works out like this:

a= |− 3 + 4 + (−5)+ 6|

= |2|

= 2

The second sum works out like this:

b= |−3|+ |4| + |−5|+ |6|

= 3 + 4 + 5 + 6

= 18

From these facts, you can conclude that for integers, the absolute value of a sum is not

necessarily equal to the sum of the absolute values.

2. The first expression simplifies like this, step-by-step:

(3+ 5) − (7 + 9) − (11 + 13) − 15

= 8 − 16 − 24 − 15

=− 47

The second expression simplifies like this, step-by-step:

3 + (5 − 7) + (9 − 11) + (13 − 15)

= 3 + (−2)+ (−2)+ (−2)

=− 3

3. When you see no parentheses in a string of sums and differences, all the numbers or
   variables are in effect “outside the parentheses,” so you should perform the operations
   straightaway from left to right. Here is the original expression:

3 + 5 − 7 + 9 − 11 + 13 − 15

In order, the sums and differences evolve as follows:

3 + 5 = 8

8 − 7 = 1

1 + 9 = 10

10 − 11 =− 1

− 1 + 13 = 12

12 − 15 =− 3

Chapter 4 595