Mathematics
Grade-8
Easy

Question

Guess the smallest rational numbers among negative 4 over 9 comma space fraction numerator 5 over denominator negative 12 end fraction comma space fraction numerator 7 over denominator negative 18 end fraction space and space fraction numerator 2 over denominator negative 3 end fraction

  1. fraction numerator 7 over denominator negative 18 end fraction
  2. negative 4 over 9
  3. fraction numerator 2 over denominator negative 3 end fraction
  4. fraction numerator 5 over denominator negative 12 end fraction

hintHint:

1. Rational numbers refer to those numbers that can be represented as a simple fraction.
2. If the denominators of 2 or more fractions are different, we find the LCM of the denominator and multiply the denominators to make them equal to the LCM and then compare the numerators.

The correct answer is: fraction numerator 7 over denominator negative 18 end fraction


    GIVEN-
    Fraction 1= -4/9
    Fraction 2= 5/-12
    Fraction 3= 7/-18
    Fraction 4= 2/-3
    TO FIND-
    Smallest rational number from the given options.
    SOLUTION-
    From the given information, we observe that-
    The denominators of all the fractions are different i.e. 3, 9, 12 & 18.
    Hence, find the LCM of 3, 9, 12 & 18 i.e. 36.
    We make the denominators equal to 36 as-
    Fraction 1 = -4/9 = -4*4 / 9*4 = -16/36 .................................... (Multiplying and dividing the fraction by 4)
    Fraction 2 = 5/-12 = -5/12 = -5*3 / 12*3 = -15/36 .................... (Multiplying and dividing the fraction by 3)
    Fraction 3 = 7/-18 = -7/18 = -7*2 / 18*2 = -14/36 .................... (Multiplying and dividing the fraction by 2)
    Fraction 4 = 2/-3 = -2/3 = -2*12 / 3*12 = -24/36 ...................... (Multiplying and dividing the fraction by 12)
    Now, that the denominators are the same, we compare the numerators as-
    -24 < -16 < -15 < -14
    ∴ 2/-3 < -4/9 < 5/-12 < 7/-18
    Hence, 2/-3 is the smallest rational number from the given option.
    FINAL ANSWER-
    Option 'a' i.e. '2/-3' is the correct answer to the given question.

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