Algebra Know-It-ALL

150 Review Questions and Answers

the primes smaller than s that divide n without leaving a remainder, we have found the prime

factors of n. Some of these prime factors may occur more than once.

Chapter 4

Question 4-1

What is the meaning of the term absolute value with respect to integers?

Answer 4-1

The absolute value is the extent to which a number differs from 0. If we imagine the integers

as points on a straight line with a “number reflector” passing through the point for 0, then the

absolute value of any integer is its distance from the “number reflector.” Figure 10-2 shows a

couple of examples. The absolute value of an integer is always positive or 0, because it is an

expression of distance without taking direction into account. The absolute value of any natural

number is equal to that natural number. The absolute value of any negative integer can be

obtained by removing the minus sign.

Question 4-2

Suppose we have two integers a and b. How can we define a+b on a vertical number line

where values increase as we move upward?

Answer 4-2

We start by finding the point on the line that corresponds to a. Then we move upward along

the line for a distance of b units. We end up at the point for a+b.

0

1

2

3

1

2

• 3


• 
  

“Number reflector” -

Absolute

value

is 3

Absolute

value

is 3

Figure 10-2 Illustration for Answer 4-1.