1.

Which of the two rational numbers is greater in the given pair? (i) \(\frac{3}{8}\)or 0 (ii) \(\frac{-2}{9}\)or 0 (iii) \(\frac{-3}{4}\)or\(\frac{1}{4}\) (iv)\(\frac{-5}{7}\) or\(\frac{-4}{7}\) (v) \(\frac{2}{3}\)or\(\frac{3}{4}\) (vi) \(\frac{-1}{2}\)or-1

Answer»

(i)\(\frac{3}{8}\) is a positive number and all positive numbers are greater than 0. 

Therefore,\(\frac{3}{8}\)> 0

(ii) \(\frac{-2}{9}\) is a negative number and all negative numbers are less than 0. 

Therefore, 0 >\(\frac{-2}{9}\)

(iii) Both \(\frac{-3}{4}\)and \(\frac{1}{4}\) have the same denominator 4. Therefore, we can directly compare both the numbers. Since, 1 > -3

Therefore, \(\frac{-3}{4}\)>\(\frac{1}{4}\)

(iv) Both \(\frac{-3}{4}\) and\(\frac{-4}{7}\) have the same denominator 7. Therefore, we can directly compare both the numbers. Since, -4 > -5

Therefore, \(\frac{-4}{7}\)>\(\frac{-5}{7}\)

(v)\(\frac{-3}{4}\) and \(\frac{-1}{4}\)have different denominators. Therefore, we take LCM of 3 and 4 that is 12.

 Now,

\( \frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}\)

And,

\( \frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}\)

Since, 9 > 8

\(\frac{9}{12}\)>\(\frac{8}{12}\)

Hence, \(\frac{2}{3}\)>\(\frac{3}{4}\)

(vi) We can write -1=\(\frac{-1}{1}\)

\(\frac{1}{2}\)and \(\frac{-1}{1}\)have different denominators.

Therefore, we take LCM of 1 and 2 that is 2.

 Now,

\( \frac{-1}{2}=\frac{-1\times1}{2\times1}=\frac{-1}{2}\)

And,

\( \frac{-1}{1}=\frac{-1\times2}{1\times2}=\frac{-2}{2}\)

Since, -1 > -2

Therefore,  \(\frac{-1}{2}\)>\(\frac{-2}{2}\)

Hence, \(\frac{-1}{2}\)>-1



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