Fractions as Rational Numbers
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Questions and Answers

What is the definition of a rational number?

  • A number that can be expressed as the quotient or fraction of two integers. (correct)
  • A number that can be expressed as a fraction of two decimals.
  • A number that can be expressed as a percentage.
  • A number that can be expressed as a decimal.

    • What is the key characteristic of a proper fraction?

  • The denominator is zero.
  • The numerator is less than the denominator. (correct)
  • The numerator is greater than the denominator.
  • The numerator is equal to the denominator.

    • What is the process of simplifying a fraction?

  • Dividing both numerator and denominator by their greatest common divisor (GCD). (correct)
  • Multiplying both numerator and denominator by the same non-zero integer.
  • Adding both numerator and denominator by the same non-zero integer.
  • Subtracting both numerator and denominator by the same non-zero integer.

    • What is the result of multiplying two fractions?

    <p>The product of the numerators over the product of the denominators.</p> Signup and view all the answers

    What is the purpose of finding a common denominator when adding or subtracting fractions?

    <p>To enable the addition or subtraction of fractions with different denominators.</p> Signup and view all the answers

    What is an equivalent fraction?

    <p>A fraction that has the same value as another fraction.</p> Signup and view all the answers

    What is a characteristic of a mixed number?

    <p>It is a combination of a whole number and a proper fraction</p> Signup and view all the answers

    Which type of fraction has a numerator greater than or equal to the denominator?

    <p>Improper fraction</p> Signup and view all the answers

    What is another name for a fraction that represents the same value as another fraction?

    <p>Equivalent ratio</p> Signup and view all the answers

    What type of decimal representation of a rational number repeats in a predictable pattern?

    <p>Recurring decimal</p> Signup and view all the answers

    What is the result of converting a mixed number?

    <p>An improper fraction</p> Signup and view all the answers

    Study Notes

    Fractions as Rational Numbers

    Definition:

    • A rational number is a number that can be expressed as the quotient or fraction of two integers, i.e., a/b where a and b are integers and b ≠ 0.

    Key Characteristics:

    • A fraction is a way to represent a rational number.
    • A fraction consists of a numerator (top number) and a denominator (bottom number).
    • The numerator and denominator are integers.
    • The denominator cannot be zero.

    Types of Fractions:

    • Proper Fractions: The numerator is less than the denominator. (e.g., 1/2, 2/3)
    • Improper Fractions: The numerator is greater than or equal to the denominator. (e.g., 3/2, 5/3)
    • Mixed Numbers: A combination of a whole number and a proper fraction. (e.g., 2 1/2, 3 3/4)

    Operations with Fractions:

    • Addition and Subtraction: Require a common denominator.
    • Multiplication: Multiply the numerators and denominators separately.
    • Division: Invert the second fraction and then multiply.

    Equivalent Fractions:

    • Two fractions are equivalent if they have the same value.
    • Can be obtained by multiplying or dividing both numerator and denominator by the same non-zero integer.

    Simplifying Fractions:

    • Divide both numerator and denominator by their greatest common divisor (GCD) to reduce a fraction to its simplest form.
    • The simplest form is also known as the lowest terms.

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    Quiz Team

    Description

    Learn about fractions, including their definition, key characteristics, types, operations, equivalent fractions, and simplification. Understand how to work with fractions, convert between types, and reduce to simplest form.

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