Mathematics
Grade-8
Easy
Question
Guess the smallest rational numbers among 
Hint:
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:
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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Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
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We know that 5040 is not a perfect square because √5040 = 12√35.
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Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
a. 5
1008 * 5 = 5040
We know that 5040 is not a perfect square because √5040 = 12√35.
b. 2
1008 * 2 = 2016
We know that 2016 is not a perfect square because √2016 = 12√14.
c. 7
1008 * 7 = 7056
We know that 7056 is a perfect square because √7056 = 84.
d. 8
1008 * 8 = 8064
We know that 8064 is not a perfect square because √8064 = 24√14.
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