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Mathematics

Fill in the blanks with the correct symbol out of >, = or < :

(i) −174\dfrac{-17}{4} …………… −154\dfrac{-15}{4}

(ii) 0 …………… −1−2\dfrac{-1}{-2}

(iii) 4−3\dfrac{4}{-3} …………… −87\dfrac{-8}{7}

(iv) −512\dfrac{-5}{12} …………… 7−16\dfrac{7}{-16}

(v) −78\dfrac{-7}{8} …………… −89\dfrac{-8}{9}

(vi) 1−10\dfrac{1}{-10} …………… −4−5\dfrac{-4}{-5}

Rational Numbers

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Answer

(i) −174\dfrac{-17}{4} < −154\dfrac{-15}{4}

(ii) 0 < −1−2\dfrac{-1}{-2}

(iii) 4−3\dfrac{4}{-3} < −87\dfrac{-8}{7}

(iv) −512\dfrac{-5}{12} > 7−16\dfrac{7}{-16}

(v) −78\dfrac{-7}{8} > −89\dfrac{-8}{9}

(vi) 1−10\dfrac{1}{-10} < −4−5\dfrac{-4}{-5}

Explanation

(i) Since the denominators are the same, we compare the numerators where -17 is less than -15.

(ii) −1−2\dfrac{-1}{-2} simplifies to the positive rational number 12\dfrac{1}{2}, and zero is always less than any positive number.

(iii) L.C.M. of 3 and 7 is 21. After converting to a common denominator of 21, we compare −2821\dfrac{-28}{21} and −2421\dfrac{-24}{21}, where -28 < -24.

(iv) L.C.M. of 12 and 16 is 48. After converting to a common denominator of 48, the fractions are −2048\dfrac{-20}{48} and −2148\dfrac{-21}{48}, and since -20 > -21, the first is greater.

(v) L.C.M. of 8 and 9 is 72. After converting to a common denominator of 72, the fractions are −6372\dfrac{-63}{72} and −6472\dfrac{-64}{72}, and -63 > -64 so −6372\dfrac{-63}{72} > −6472\dfrac{-64}{72}.

(vi) 1−10\dfrac{1}{-10} is a negative rational number while −4−5\dfrac{-4}{-5} is positive, and any negative number is less than a positive one.

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