Rational Numbers Quiz
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Questions and Answers

What is the value of (\frac{7}{3} + \frac{-2}{3} - \frac{5}{6})?

  • \frac{3}{2}
  • \frac{1}{3}
  • 1
  • \frac{13}{6} (correct)

    • The sum of two rational numbers is always irrational.

    False

    Find an equivalent rational number for (\frac{-4}{5}) by multiplying both the numerator and denominator by -2.

    \frac{8}{-10}

    To find the LCM of 6 and 8, we need to list the multiples of both numbers and find the _______________ multiple that is common to both.

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

    Match the following rational numbers with their properties:

    <p>\frac{5}{2} = Has a terminating decimal expansion \frac{3}{4} = Has a recurring decimal expansion \frac{-4}{5} = Is in the simplest form \frac{7}{6} = Has a mixed decimal expansion</p> Signup and view all the answers

    Which of the following is a rational number?

    <p>3/4</p> Signup and view all the answers

    Every integer is a rational number.

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

    Simplify and express in standard form: -36/54

    <p>-2/3</p> Signup and view all the answers

    The additive inverse of 5/7 is ___________________.

    <p>-5/7</p> Signup and view all the answers

    Match the following rational numbers with their equivalent forms:

    <p>4/5 = 8/10 3/4 = 6/8 2/3 = 4/6 5/6 = 10/12</p> Signup and view all the answers

    What is the value of x in the equation: 3/5 = 15/x

    <p>15</p> Signup and view all the answers

    The sum of two rational numbers is always a rational number.

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

    Arrange the following rational numbers in ascending order: 3/7, -5/6, -2/3, 1/2

    <p>-5/6, -2/3, 3/7, 1/2</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.
    • Every integer is a rational number.

    Standard Form of Rational Numbers

    • The standard form of a rational number is the form in which the numerator and denominator have no common factors other than 1.
    • Example: The standard form of -45/60 is -3/4.

    Additive Inverse of Rational Numbers

    • The additive inverse of a rational number is the number that when added to it, results in zero.
    • Example: The additive inverse of 5/7 is -5/7.

    Equivalent Rational Numbers

    • Equivalent rational numbers are numbers that have the same value.
    • Example: 4/5, 8/10, and 20/25 are equivalent rational numbers.

    Comparing Rational Numbers

    • To compare two rational numbers, we can convert them to equivalent fractions with the same denominator.
    • Example: To compare 3/7, -5/6, -2/3, and 1/2, we can convert them to equivalent fractions with the same denominator.

    Operations with Rational Numbers

    • The sum of two rational numbers is always a rational number.
    • The additive inverse of a negative rational number is always positive.
    • Rational numbers are not closed under division.

    Simplifying Rational Expressions

    • Simplifying a rational expression involves dividing both the numerator and denominator by their greatest common divisor.
    • Example: Simplifying -36/54 gives -2/3.

    Solving Equations with Rational Numbers

    • To solve an equation with rational numbers, we can use the properties of equivalent fractions.
    • Example: Solving 3/5 = 15/x gives x = 25.

    Plotting Rational Numbers on a Number Line

    • Rational numbers can be plotted on a number line by converting them to equivalent decimals.
    • Example: Plotting 1/4, -3/4, and 5/8 on a number line involves converting them to equivalent decimals.

    Applications of Rational Numbers

    • Rational numbers can be used to solve real-world problems, such as calculating the total cost of items.
    • Example: Calculating the total cost of 3 sandwiches and 2 drinks, where the cost of a sandwich is 5/2 dollars and the cost of a drink is 3/4 dollars.

    Finding the Least Common Multiple (LCM) of Denominators

    • To find the LCM of denominators, we can list the multiples of each denominator and find the common multiple.
    • Example: Finding the LCM of 6 and 8 involves listing the multiples of 6 and 8 and finding the common multiple, which is 24.

    Adding Rational Numbers with Different Denominators

    • To add rational numbers with different denominators, we can use the LCM method.
    • Example: Adding 5/6 and 7/8 using the LCM method involves finding the LCM of 6 and 8, which is 24, and then converting the fractions to equivalent fractions with the same denominator.

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    Test your understanding of rational numbers with these questions on identifying rational numbers, standard form, and additive inverses.

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