Rational Numbers Quiz
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Rational Numbers Quiz

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Questions and Answers

What is the absolute value of a rational number?

  • It represents the distance from zero on the number line. (correct)
  • It can never be negative.
  • It can be zero, but never negative.
  • It is always greater than zero.

    • Which of the following sets does NOT include rational numbers?

  • The set of natural numbers ($\mathbb{N}$)
  • The set of integers ($\mathbb{Z}$)
  • The set of whole numbers
  • The set of real numbers ($\mathbb{R}$) (correct)

    • What correctly represents the relationship among the sets W, ℤ, and ℚ?

  • Every rational number can be expressed as a fraction of two integers. (correct)
  • Integers include both positive and negative rational numbers only.
  • Natural numbers encompass all integers and rational numbers.
  • All natural numbers are integers but not all integers are rational.

    • On a number line, which of the following statements about rational numbers is true?

    <p>Every point on a number line is either a rational or an irrational number.</p> Signup and view all the answers

    Which of the following statements best describes a rational number?

    <p>It can be represented as a decimal that terminates or repeats.</p> Signup and view all the answers

    Which option correctly defines the set ℤ?

    <p>It includes all positive and negative whole numbers.</p> Signup and view all the answers

    What is a necessary condition for a number to be classified as rational?

    <p>It must be expressible as a ratio of two integers.</p> Signup and view all the answers

    What is the definition of a rational number?

    <p>A number that can be represented as a fraction of two integers.</p> Signup and view all the answers

    Which of the following fractions represents a rational number?

    <p>$\frac{7}{3}$</p> Signup and view all the answers

    How should improper fractions be represented on a number line?

    <p>They should first be converted to mixed fractions.</p> Signup and view all the answers

    Where are negative rational numbers located on a number line?

    <p>They are located to the left of zero.</p> Signup and view all the answers

    Which of the following is NOT a rational number?

    <p>√2</p> Signup and view all the answers

    Where do positive proper fractions exist on a number line?

    <p>Between zero and one.</p> Signup and view all the answers

    What is the representation of the rational number $\frac{2}{5}$ on the number line?

    <p>It is between 0 and 1.</p> Signup and view all the answers

    What is the set of all rational numbers denoted by?

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

    How would you locate the number $\frac{3}{2}$ on a number line?

    <p>It lies between 1 and 2.</p> Signup and view all the answers

    What is the result of the expression $4 - 2$?

    <p>$2$</p> Signup and view all the answers

    Calculate the difference of $−5.3 − 3.45$.

    <p>$−8.75$</p> Signup and view all the answers

    Determine the value of $y - ( + 5)$ when $y = 4$.

    <p>$−1$</p> Signup and view all the answers

    Find the remaining length of the rope after cutting off pieces of lengths $4$ m and $7$ m from a $23$ m rope.

    <p>$12$ m</p> Signup and view all the answers

    What is the weight of the bananas if the total weight is $58$ kg, $11$ kg is apples, and $18$ kg is oranges?

    <p>$29$ kg</p> Signup and view all the answers

    Evaluate $15 - (−y - 2)$ when $y = 7$.

    <p>$20$</p> Signup and view all the answers

    What is the result of multiplying $7/5$ by $11/3$?

    <p>$77/15$</p> Signup and view all the answers

    What is $−3 − 2$?

    <p>$−5$</p> Signup and view all the answers

    What property is illustrated when rewriting the equation by grouping terms differently?

    <p>Associative property</p> Signup and view all the answers

    In the equation involving sums, if $a + b = c$, which of the following is also true?

    <p>$0 + c = c$</p> Signup and view all the answers

    Using the properties of addition, how is $(a + b) + c$ equivalent to $a + (b + c$)?

    <p>Through the Associative property</p> Signup and view all the answers

    What does the equation $a + (-b) = 0$ represent in terms of properties?

    <p>Additive inverse</p> Signup and view all the answers

    When calculating the sum of $3, 5,$ and $6$ using properties of addition, the result must always equal?

    <p>14</p> Signup and view all the answers

    Which equation shows the application of the Communicative property?

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

    If $a + b = c$ and $b + a$ is calculated, which outcome is expected?

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

    In the example provided, when $3 + 5 + 6$ is computed, which sequence follows the Associative property correctly?

    <p>Both A and B</p> Signup and view all the answers

    What should be done first when adding two rational numbers with different signs?

    <p>Take the sign of the addend with the greater absolute value.</p> Signup and view all the answers

    In the operation −9 + 4, which sign should be chosen for the result?

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

    For the operation −5 + 3, what is the final result?

    <p>−2</p> Signup and view all the answers

    What is the absolute value of the result for the operation −6 + 4?

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

    How do you determine the sign of the result when adding −5 and 4?

    <p>Compare the absolute values and take the sign of −5.</p> Signup and view all the answers

    When combining −5 + 3, what is the correct calculation to find the difference of the absolute values?

    <p>5 − 3</p> Signup and view all the answers

    In the expression −5 + 3, what is the correct final result?

    <p>−1</p> Signup and view all the answers

    Study Notes

    Rational numbers

    • A number that can be written in the form of a/b, where a and b are integers and b ≠ 0, is called a rational number.
    • Rational numbers are represented by the symbol ℚ, where ℚ ⊂ ℤ ⊂ ℕ.
    • Rational numbers with a positive sign are located on the right side of zero on a number line, and rational numbers with a negative sign are located on the left side of zero.
    • Proper fractions are located between 0 and 1 on the number line.
    • Improper fractions are located on the number line by first converting them to mixed fractions.
    • Mixed fractions are located on the number line by first converting them to improper fractions.
    • To find the sum of two rational numbers with different signs, follow these steps:
      • Take the sign of the addend with the greater absolute value.
      • Subtract the absolute value of the smaller addend from the absolute value of the larger addend.
      • Put the sign of the larger addend in front of the difference.
    • Rational numbers can be expressed as decimals and are either terminating or repeating.
    • To multiply any two rational numbers, multiply the numerators and the denominators.
    • To add or subtract rational numbers with different denominators, a common denominator must be found.
    • The additive identity of rational numbers is 0.
    • The multiplicative identity of rational numbers is 1.
    • To find the difference between two rational numbers, the smaller rational number is subtracted from the larger rational number.

    Properties of Rational Numbers

    • Closure Property: For any two rational numbers a and b, a + b and a × b are also rational numbers.
    • Associative Property: For any three rational numbers a, b and c, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).
    • Commutative Property: For any two rational numbers a and b, a + b = b + a and a × b = b × a.
    • Distributive Property: For any three rational numbers a, b and c, a × (b + c) = a × b + a × c.
    • Identity Property: 0 is the additive identity and 1 is the multiplicative identity.
    • Inverse Property: Each rational number has an additive inverse and each non-zero rational number has a multiplicative inverse.

    Absolute Value of Rational Numbers

    • The absolute value of a rational number 'a' is denoted as '│a│' and it represents the distance of 'a' from 0 on the number line.
    • The absolute value of a non-zero rational number is always positive.
    • The absolute value of 0 is 0.

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    G8 U1-3 Rational Numbers PDF

    Description

    Test your understanding of rational numbers with this quiz. Explore their definitions, representations, and how to perform operations with them. Dive into the distinctions between proper and improper fractions as well as mixed fractions.

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