Lecture 12
Rational Numbers

Definitions:

Rational Numbers: { | a Integer Numbers, b Integer Numbers, and b ≠ 0 }.

N { x | x Natural Numbers }

W { x | x Whole Numbers }

Z { x | x Integer Numbers }

Q { x | x Rational Numbers }

Therefore

The capital letter can be used to represent the associate set.

For instance:

99 N, since 99 is a Natural Number.

For instance:

0 W, since 0 is a Whole Number.

For instance:

-125 Z, since -125 is an Integer Number.

For instance:

Q, since is a Rational Number.

Objectives:

· To understand Rational Numbers.

· To identify elements of the set of Rational Numbers.

· To explain why a number is a Rational Number.

Examples:

1. Is a rational number?

Yes, a = 3 Z and b = 4 Z and b ≠ 0,

2. Is a rational number?

Yes, a = -3 Z and b = 100 Z and b ≠ 0,

3. Is a rational number?

Yes, a = 0 Z and b = 5 Z and b ≠ 0,

4. Is 7 a rational number?

Yes, since 7 = , a = 7 Z and b = 1 Z and b ≠ 0,

Exercises:

1. Is a rational number?

2. Is a rational number?

3. Is a rational number?

4. Is -6 a rational number?

5. Is a rational number?

6. Is a rational number?

7. Is a rational number?

Solutions:

1. Is a rational number?

Yes, a = 6 Z and b = 11 Z and b ≠ 0,

2. Is a rational number?

Yes, a = - 5 Z and b = 11 Z and b ≠ 0,

3. Is a rational number?

Yes, a = 0 Z and b = 5 Z and b ≠ 0,

4. Is -6 a rational number?

Yes, since - 6 = , a = - 6 Z and b = 1 Z and b ≠ 0,

5. Is a rational number?

No, since b = 0, .

6. Is a rational number?

No, since b = 0, .

7. Is a rational number?

Yes, since = , a = 2 Z and b = 1 Z and b ≠ 0,