The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 2.1: CLASSIFYING COUNTING NUMBERS, WHOLE

NUMBERS, INTEGERS, AND RATIONAL NUMBERS

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Numbers can be classified into various groups. Four of the most important groups are shown

below:

• Counting numbers:Starting with 1, the counting numbers continue forever by adding 1
  to the previous number: 1, 2, 3, 4, 5,...


• Whole numbers:Zero and the counting numbers make up the whole numbers: 0, 1, 2, 3,
  4, 5,...


• Integers:The counting numbers, their opposites, and zero make up the integers:...−3,
  −2,−1, 0, 1, 2, 3,...


• Rational numbers:Any number that can be written as the quotient of two integers make
  up the rational numbers.

EXAMPLES

3,−1, 0,

3

5

,−

7

8

,4. 1

Many numbers belong to several groups, but some belong to only one group. 5, for example,

is a counting number, whole number, integer, and rational number. The fraction

3

5

can be

classified only as a rational number.

DIRECTIONS: Classify each number below.

15 − 80 − 74

1

1

3

− 3

1

5

− 1

3

5

− 150

0.6 − 1. 821

CHALLENGE:Do you agree with the following statement? All integers are

rational numbers but only some rational numbers are integers. Explain

your answer.

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Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.