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Questions and Answers

What is the mid-point of the line segment joining the points $\frac{5}{10}$ and $\frac{6}{10}$?

  • $\frac{3}{5}$
  • $\frac{11}{20}$ (correct)
  • $\frac{1}{5}$
  • $\frac{1}{2}$
  • How many rational numbers can be found between any two rational numbers?

  • None
  • Infinitely many (correct)
  • Only one
  • Exactly two
  • Which of the following represents a rational number between $\frac{2}{7}$ and $\frac{6}{7}$?

  • $\frac{7}{8}$
  • $\frac{4}{7}$ (correct)
  • $\frac{5}{7}$ (correct)
  • $\frac{1}{3}$
  • What can be concluded about the integers m and m + 1 where m is an integer?

    <p>There is no integer between them</p> Signup and view all the answers

    If the points on the number line are $\frac{1}{10}$ and $\frac{1}{20}$, what is their mid-point?

    <p>$\frac{1}{15}$</p> Signup and view all the answers

    What is the denominator of the rational number that lies between $\frac{3}{5}$ and $\frac{4}{5}$?

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

    Which of the following best describes rational numbers in relation to integers?

    <p>All integers are rational numbers</p> Signup and view all the answers

    Which of the following is an incorrect representation of a rational number between $\frac{-3}{4}$ and $\frac{5}{4}$?

    <p>$\frac{5}{4}$</p> Signup and view all the answers

    What fraction can be represented as a decimal by moving the decimal point two places to the left?

    <p>1.350</p> Signup and view all the answers

    Which of the following statements about adding zeros to decimal fractions is true?

    <p>It keeps the value of the fraction the same.</p> Signup and view all the answers

    What is the first step to convert the fraction $\frac{7}{4}$ into a decimal?

    <p>Perform the division to find the quotient.</p> Signup and view all the answers

    What will be the decimal representation for the rational number $\frac{11}{5}$?

    <p>2.1</p> Signup and view all the answers

    When multiplying a decimal fraction by 1000, where does the decimal point move?

    <p>Three places to the right</p> Signup and view all the answers

    If 1.35 is expressed as 001.35, what is the decimal form of it?

    <p>0.0135</p> Signup and view all the answers

    Which process will lead to the correct conversion of $\frac{2}{5}$ into decimal form?

    <p>Divide 2 by 5.</p> Signup and view all the answers

    What is the result of dividing a positive integer by a negative integer?

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

    What is the quotient of two negative integers?

    <p>Positive number</p> Signup and view all the answers

    Which equation correctly explains the division of 7 by -2?

    <p>$\frac{7}{-2} = -3.5$</p> Signup and view all the answers

    What happens when zero is used as a denominator in a division?

    <p>It results in an undefined value</p> Signup and view all the answers

    If -13 is divided by -2, what is the result?

    <p>6.5</p> Signup and view all the answers

    How is the division of a positive integer by a negative integer expressed?

    <p>It can be written as a negative fraction with a positive denominator.</p> Signup and view all the answers

    What is the relationship between multiplication and division rules of integers according to the content?

    <p>They have similar rules except for zero.</p> Signup and view all the answers

    Which of these statements is true regarding the quotient of two positive integers?

    <p>It is always a positive number.</p> Signup and view all the answers

    What is the highest common factor (HCF) of the numbers 195, 312, and 546?

    <p>39</p> Signup and view all the answers

    Using the prime factorization method, what is the HCF of 10, 15, and 12?

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

    When finding the HCF of 60, 12, and 36, what prime factorization leads to the HCF?

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

    What is the HCF of any two consecutive even numbers?

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

    In the division method for finding HCF of 144 and 252, what is the last divisor before the remainder becomes zero?

    <p>36</p> Signup and view all the answers

    To find the HCF of three numbers using prime factorization, what must be identified?

    <p>The common factors</p> Signup and view all the answers

    Which statement about the HCF is true?

    <p>It is the largest number that divides all the given numbers.</p> Signup and view all the answers

    What are opposite rays?

    <p>Two rays that have the same origin and form a straight line.</p> Signup and view all the answers

    In figure (i), which angles are formed by ray BC and ray BA?

    <p>Obtuse angle</p> Signup and view all the answers

    What is the sum of the measures of angles in a linear pair?

    <p>180°</p> Signup and view all the answers

    What distinguishes adjacent angles from non-adjacent angles?

    <p>Adjacent angles have a common arm and non-adjacent do not.</p> Signup and view all the answers

    Which of the following pairs of angles form a linear pair?

    <p>Two angles that have a common arm and their other arms form a straight line.</p> Signup and view all the answers

    Which arms of angles ∠PQR and ∠RQS are not common?

    <p>PR and QS</p> Signup and view all the answers

    Are ray PM and ray PT opposite rays?

    <p>No, because they do not form a straight line.</p> Signup and view all the answers

    If the measure of angle ∠PQR is 70°, what is the measure of angle ∠RQS?

    <p>110°</p> Signup and view all the answers

    What is an effect of converting rational numbers into equivalent fractions with larger denominators?

    <p>It increases the number of rational numbers that can be expressed between them.</p> Signup and view all the answers

    If you multiply the numerator and denominator of a fraction by the same number, what happens to its value?

    <p>The value of the fraction remains unchanged.</p> Signup and view all the answers

    What is the result of converting the rational numbers $\frac{1}{2}$ and $\frac{3}{5}$ into equivalent fractions with a common denominator before identifying numbers between them?

    <p>It makes the fractions easier to compare directly without altering their values.</p> Signup and view all the answers

    Which set of rational numbers lies between $\frac{7}{14}$ and $\frac{8}{14}$ when their denominators are increased to 140?

    <p>$\frac{71}{140}$ and $\frac{79}{140}$</p> Signup and view all the answers

    What is the general pattern observed when rational numbers are expressed with increasingly larger denominators?

    <p>More rational numbers emerge between the two fractions.</p> Signup and view all the answers

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