Lesson 1.1: Classifying Rational Numbers
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Questions and Answers

What is the definition of rational numbers?

Numbers that can be written as a fraction. Includes decimals that end or repeat with a pattern.

What is the definition of integers?

Positive and negative numbers (including 0) that do not have fractions or decimals.

What is the definition of whole numbers?

Any positive number (including zero) that does not have a fraction or decimal.

What is the definition of natural numbers?

<p>Positive numbers without fractions or decimals not including zero. Also known as counting numbers.</p> Signup and view all the answers

Classify the following number: 36

<p>Rational, integer, whole, natural</p> Signup and view all the answers

Classify the following number: -29

<p>Rational, integer</p> Signup and view all the answers

Classify the following number: -2.6

<p>Rational</p> Signup and view all the answers

Classify the following number: 0

<p>Rational, integer, whole</p> Signup and view all the answers

All rational numbers are whole numbers.

<p>False</p> Signup and view all the answers

All whole numbers are rational numbers.

<p>True</p> Signup and view all the answers

Some integers are also whole numbers.

<p>True</p> Signup and view all the answers

All integers are whole numbers.

<p>False</p> Signup and view all the answers

All natural numbers are rational numbers.

<p>True</p> Signup and view all the answers

All rational numbers are natural numbers.

<p>False</p> Signup and view all the answers

Some integers are natural numbers.

<p>True</p> Signup and view all the answers

All natural numbers are integers.

<p>True</p> Signup and view all the answers

All rational numbers are whole numbers.

<p>False</p> Signup and view all the answers

Some whole numbers are rational numbers.

<p>True</p> Signup and view all the answers

All integers are rational numbers.

<p>True</p> Signup and view all the answers

Some rational numbers are integers.

<p>True</p> Signup and view all the answers

All whole numbers are natural numbers.

<p>False</p> Signup and view all the answers

All natural numbers are whole numbers.

<p>True</p> Signup and view all the answers

Study Notes

Rational Numbers

  • Defined as numbers that can be expressed as a fraction.
  • Includes decimals that either terminate or repeat with a pattern.

Integers

  • Comprise positive and negative whole numbers, including zero.
  • Do not include fractions or decimals.

Whole Numbers

  • Any positive number, including zero.
  • Excludes fractions and decimals.

Natural Numbers

  • Positive numbers that don't have fractions or decimals, starting from one.
  • Also referred to as counting numbers.

Classification of Numbers

  • 36: Classifies as rational, integer, whole, and natural.
  • -29: Classifies as rational and integer only.
  • -2.6: A rational number.
  • 0: Classifies as rational, integer, and whole.

True/False Statements Analysis

  • Not all rational numbers are whole numbers (e.g., rational numbers can include fractions).
  • All whole numbers are rational numbers, as they can be expressed as fractions (e.g., 5/1).
  • Some integers are also whole numbers (e.g., 5).
  • Not all integers are whole numbers (e.g., -5).
  • All natural numbers are rational numbers, being subsets of them.
  • Not all rational numbers are natural numbers (e.g., 2.5).
  • Some integers are natural numbers (e.g., 3).
  • All natural numbers are integers, consisting solely of non-negative whole numbers.
  • Not all whole numbers are natural numbers due to the inclusion of zero.
  • All natural numbers fit within the whole numbers classification.

Summary of Relationships

  • Whole numbers are a subset of rational numbers.
  • Rational numbers encompass integers, while integers consist of both whole numbers and negative numbers.

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