Adding Rational Numbers
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Questions and Answers

What is a fundamental property of rational numbers?

  • They always have a terminating decimal expansion.
  • They are always prime numbers.
  • They are never negative.
  • They can be expressed as a quotient or fraction of two integers. (correct)

    • What is the first step in adding two rational numbers?

  • Multiply the fractions together.
  • Find a common denominator (LCD) for the two fractions. (correct)
  • Add the numerators and keep the same denominator.
  • Subtract the denominators and keep the same numerator.

    • How do you subtract two rational numbers?

  • Multiply the fractions together and then subtract.
  • Add the numerators and keep the same denominator.
  • Divide the two fractions.
  • Find a common denominator, convert both fractions, and then subtract the numerators. (correct)

    • What is the result of multiplying two rational numbers?

    <p>A fraction with the product of the numerators and the product of the denominators.</p> Signup and view all the answers

    How do you divide two rational numbers?

    <p>Invert the second fraction and then multiply.</p> Signup and view all the answers

    Why is it essential to simplify the resulting fraction when performing arithmetic operations with rational numbers?

    <p>To ensure the fraction is in its simplest form.</p> Signup and view all the answers

    What is a key rule to keep in mind when adding or subtracting rational numbers?

    <p>Always find a common denominator.</p> Signup and view all the answers

    What is true about the decimal expansion of rational numbers?

    <p>It is always finite or recurring.</p> Signup and view all the answers

    Study Notes

    Properties of Rational Numbers

    • A rational number is a number that can be expressed as the quotient or fraction of two integers (p/q), where q ≠ 0.
    • Rational numbers can be expressed in decimal form, and the decimal expansion is finite or recurring.
    • Rational numbers satisfy the usual rules of arithmetic, including commutativity, associativity, and distributivity.

    Adding Rational Numbers

    • To add two rational numbers, find a common denominator (LCD) for the two fractions.
    • Convert both fractions to have the LCD.
    • Add the numerators and keep the same denominator.

    Subtracting Rational Numbers

    • To subtract two rational numbers, find a common denominator (LCD) for the two fractions.
    • Convert both fractions to have the LCD.
    • Subtract the numerators and keep the same denominator.

    Multiplying Rational Numbers

    • To multiply two rational numbers, multiply the numerators.
    • Multiply the denominators.
    • Simplify the resulting fraction, if possible.

    Dividing Rational Numbers

    • To divide two rational numbers, invert the second fraction (flip the numerator and denominator).
    • Multiply the fractions.
    • Simplify the resulting fraction, if possible.

    Important Note

    • When performing arithmetic operations with rational numbers, it's essential to simplify the resulting fractions to their simplest form.

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    Description

    Learn how to add rational numbers, including finding a common denominator and following the rules of arithmetic. Practice with this quiz to master the concept of rational numbers.

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