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Rational Numbers Test - 14

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Rational Numbers Test - 14
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  • Question 1
    1 / -0
    Express 125625\dfrac{-125}{625} as a rational number with smallest positive denominator equal to
    Solution
    125625=15  {125×5=625}\cfrac{-125}{625} = \cfrac{-1}{5} \; \left\{ \because 125 \times 5 = 625 \right\}
  • Question 2
    1 / -0
    Express 126196\dfrac{126}{-196} as a rational number with denominator equal to 1414 then value of numerator will be
    Solution
    126196=126196\cfrac{126}{-196} =-\cfrac{126}{196}

                 =9×1414×14 = -\cfrac{9 \times 14}{14 \times 14}

                 =914 = \cfrac{-9}{14}
  • Question 3
    1 / -0
    pq\dfrac {p}{q} is a rational number when
    Solution
    By the definition of rational number, pq\dfrac{p}{q} is rational where pp and qq are integers and qq is not equal to zero.
    In all three options except A, q=0q=0.
    Hence, p=0,q0p=0, q\ne 0 is true.
  • Question 4
    1 / -0
    In the number line, the rational numbers represented by A'A' is

    Solution
    Consider the given figure,
    Distance between 00 to 33 is divided in equal 88 part
     
    So, each part is equal to =38=\dfrac{3}{8}

    Hence, point AA is at =38=\dfrac{3}{8}unit

    Hence, this is the answer.

  • Question 5
    1 / -0
    Between two rational numbers, there exists-
    Solution

    Between two rational numbers there are infinitely many rational number for example between 44 and 55 there are 4.1,4.2,.4.22,4.223.....4.1, 4.2, .4.22, 4.223 .....
    Hence, (C)(C) is the correct answer.
  • Question 6
    1 / -0
    A rational number is defined as a number that can be expressed in the form pq\dfrac{p}{q} where pp and qq are integers and 
    Solution
    According to the definition of a rational number, it can be expressed in the form of pq\dfrac{p}{q}, where pp and qq are integers and qq\neq0
  • Question 7
    1 / -0
    How many rational numbers are there between two rational numbers?
    Solution
    Consider a&ba\,\&\,b as rational numbers
    Then a rational number n1n_1 can be find in between a&ba\,\&\,b such that a<n1<ba<n_1<b
    using the formula  n1=a+b2n_1=\dfrac{a+b}{2}

    similarly, again we can find a rational number between a&n1a\,\&\,n_1 and n1&bn_1\,\&\,b
    and so on...

    Hence, between any two distinct rational numbers there are infinitely many rational numbers.
  • Question 8
    1 / -0
    Reciprocal of the fraction 23\dfrac{2}{3}is:
    Solution

  • Question 9
    1 / -0
    In the standard form of a rational number, the common factor of numerator and denominator is always:
    Solution
    According to the definition, the common factor of numerator and denominator is always 11.
  • Question 10
    1 / -0
    Which of the following numbers is the greatest?
    Solution
    The given numbers are 12, 0, 12, and 2\dfrac{-1}{2},\ 0,\ \dfrac{1}{2},\text{ and } -2

    We can write 00 and 2-2 as 01\dfrac{0}{1} and 21\dfrac{-2}{1} respectively.

    For comparing all the 44 rational numbers, we have to make their denominators same.

    Hence, multiplying 22\dfrac{2}{2} with 01 and 21\dfrac{0}{1}\ and\ \dfrac{-2}{1}.

    Now, the numbers will be:
    12, 02, 12 and 42\dfrac{-1}{2},\ \dfrac{0}{2},\ \dfrac{1}{2}\ and\ \dfrac{-4}{2}

    Comparing the numerators, we get:
    4<1<0<1-4<-1<0<1

    Hence, the rational number with numerator 11 is the greatest.
     
    Hence, 12\dfrac{1}{2} is the greatest of all the given numbers.
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