LESSON

How can you classify rational numbers?

Classifying Rational Numbers2.1

Texas Essential Knowledge and Skills

The student is expected to:

Number and operations—6.2.A

Classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers.

Number and operations—6.2.EExtend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0.

Mathematical Processes

6.1.G

Display, explain, and justify mathematical ideas and arguments using precisemathematical language in written or oral communication.

ADDITIONAL EXAMPLE 1

A

B

C

D

Write each rational number as .

ADDITIONAL EXAMPLE 2Use the Venn diagram to determine to which set or sets each number belongs. Place the numbers in the Venn diagram.

106whole numbers, integers, rational numbers

A

–5integers, rational numbers

B

ADDITIONAL EXAMPLE 2Use the Venn diagram to determine to which set or sets each number belongs. Place the numbers in the Venn diagram.

rational numbers

C

–0.4rational numbers

D

2.1 LESSON QUIZ

2 pounds must be evenly divided among 10 bags. This represents the division 2 ÷ 10.

1. There are 2 pounds of peanuts to be divided evenly into 10 bags.

a. How does this situation represent division?

b. What fraction of a pound of peanuts will each bag get?

6.2.A, 6.2.E

–272.

163.

0.154.

Write each rational number as .

5.

Write each rational number as .

Use the Venn diagram to determine in which set or sets each number belongs. Place the numbers in the Venn diagram.

186.

Whole Numbers, Integers, Rational Numbers

–177.

Integers, Rational Numbers

Use the Venn diagram to determine in which set or sets each number belongs. Place the numbers in the Venn diagram.

–2.38.

Rational Numbers

9.

Rational Numbers

Use this activity to extend student understanding of sets, subsets, and Venn diagrams. Have students complete the Venn diagram by placing the numbers from 1 to 20 in the correct part of the diagram.

How can you classify rational numbers?

You classify numbers according to their characteristics. Rational numbers can be written as a quotient of two integers, so rational numbers can be fractions, decimals, integers, or whole numbers.