Rational numbers can be positive or negative.

RATIONAL

A ratio is used to compare two numbers.

A fraction compares parts (the numerator) to the whole (the denominator).

\( \dfrac{3}{4} \displaystyle{ \longleftarrow \text{ parts} \atop \longleftarrow \text{ whole}} \)

The rational numbers can also be represented using a diagram similar to the diagram for the integers.

Rational Numbers 

• All integers are rational numbers because they can be rewritten with a denominator of one.
  For example, \(-3 = \frac{-3}{1}\) and \(4=\frac{4}{1}\).
• Most fractions are not integers, so we represent all other fractions outside of the collection of integers.
  For example, \(\frac{2}{3}\) is a rational number, but it is not an integer.
• All rational numbers are enclosed within an oval to represent that they are all a part of the rational numbers collection.

Group 1

• \(0\), \(1\), \(102\)
  \(2\) ,\(71\), \(89\)
  \(34\), \(58\)
  \(1008\)

Whole Numbers

Integers

Rational Numbers

Group 2

• \(2\), \(-5\)
  \(-8\), \(23\)
  \(-6\), \(125\)
  \(-1586\)

Integers

Rational Numbers

Group 3

• \(\frac{9}{1}\),\(-2\)
  \(6\), \(-4\), \(-\frac{1}{2}\)
  \(\frac{11}{3}\), \(\frac{5}{7}\)
  \(-100\)

Rational Numbers