Rational Numbers Basics
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Questions and Answers

What is the definition of a rational number?

  • A real number that can be expressed as a repeating decimal
  • A real number that can be expressed as the ratio of two integers (correct)
  • A real number that can be expressed as an irrational number
  • A real number that can be expressed as a finite decimal
  • What is the notation for rational numbers?

  • a / b (correct)
  • a × b
  • a - b
  • a + b
  • Which of the following operations is not allowed on rational numbers?

  • Multiplication
  • Division by zero (correct)
  • Subtraction
  • Addition
  • Which of the following numbers is a rational number?

    <p>22/7</p> Signup and view all the answers

    What is the condition for two ratios to be equivalent?

    <p>ad = bc</p> Signup and view all the answers

    How can a rational number be simplified?

    <p>By dividing both numerator and denominator by their greatest common divisor</p> Signup and view all the answers

    Study Notes

    Definition

    A rational number is a real number that can be expressed as the ratio of two integers, i.e., a fraction.

    Notation

    Rational numbers can be written in the form:

    a/b

    where a and b are integers, and b is non-zero.

    Properties

    • The set of rational numbers is denoted by Q.
    • Rational numbers can be added, subtracted, multiplied, and divided (except by zero).
    • Rational numbers are closed under these operations, meaning that the result of performing these operations on rational numbers is always a rational number.

    Examples

    • 3/4 is a rational number.
    • 22/7 is a rational number.
    • 0.5 is a rational number, since it can be written as 1/2.
    • π (pi) is not a rational number, since it cannot be expressed as a finite decimal or fraction.

    Equivalent Ratios

    • Two ratios a/b and c/d are equivalent if ad = bc.
    • For example, 1/2 and 2/4 are equivalent ratios.

    Simplification

    • A rational number can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
    • For example, 6/8 can be simplified to 3/4.

    Ordering

    • Rational numbers can be compared and ordered using the usual rules for fractions.
    • For example, 1/2 < 2/3, since 3(1) < 2(2).

    Definition of Rational Numbers

    • A rational number is a real number that can be expressed as a ratio of two integers, or a fraction.

    Notation of Rational Numbers

    • Rational numbers can be written in the form a/b, where a and b are integers and b is non-zero.

    Properties of Rational Numbers

    • The set of rational numbers is denoted by Q.
    • Rational numbers can be added, subtracted, multiplied, and divided (except by zero).
    • Rational numbers are closed under these operations, meaning the result is always a rational number.

    Examples of Rational Numbers

    • 3/4 is a rational number.
    • 22/7 is a rational number.
    • 0.5 is a rational number, since it can be written as 1/2.
    • π (pi) is not a rational number, since it cannot be expressed as a finite decimal or fraction.

    Equivalent Ratios

    • Two ratios a/b and c/d are equivalent if ad = bc.
    • For example, 1/2 and 2/4 are equivalent ratios.

    Simplification of Rational Numbers

    • A rational number can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
    • For example, 6/8 can be simplified to 3/4.

    Ordering of Rational Numbers

    • Rational numbers can be compared and ordered using the usual rules for fractions.
    • For example, 1/2 < 2/3, since 3(1) < 2(2).

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    Quiz Team

    Description

    Learn about rational numbers, their notation, and properties, including their ability to be added, subtracted, multiplied, and divided.

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