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Question

Mathematics Question on Need For Rational Numbers

Fill in the boxes with the correct symbol out of >, <, and =.
(i) -57\frac{5}{7}__ 23\frac{2}{3} (ii) -45\frac{4}{5}__-57\frac{5}{7} (iii) -78\frac{7}{8} __14−16\frac{14}{-16} (iv) −85\frac{-8}{5} __−74\frac{-7}{4}(v) 1−3\frac{1}{-3} __−14\frac{-1}{4} (vi)5−11\frac{5}{-11} −511\frac{-5}{11} (vii) 0 −76\frac{-7}{6}

Answer

(i) -57\frac{5}{7}__ 23\frac{2}{3}
−57-\frac{5}{7} = −5×37×3\frac{-5\times 3}{7\times 3} = −1521\frac{-15}{21}
23\frac{2}{3} = 2×73×7\frac{2\times7}{3\times 7} =1421\frac{14}{21}
As - 15 < 14,
Therefore, -57\frac{5}{7}<23\frac{2}{3}

(ii)-45\frac{4}{5}__-57\frac{5}{7}
-45\frac{4}{5} = -4×75×7\frac{4\times7}{5\times 7} = −2835-\frac{28}{35}
−57-\frac{5}{7} = −5×55×7-\frac{5\times5}{5\times 7} =−2535-\frac{25}{35}
As - 28 < - 25
Therefore, −45-\frac{4}{5} < −57-\frac{5}{7}