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Mathematics

Replace '653\boxed{\phantom{653}}' by an appropriate symbol '< or >' between the given fractions:

(i) 566531315\dfrac{5}{6} \boxed{\phantom{653}} \dfrac{13}{15}

(ii) 45\dfrac{4}{5} 653\boxed{\phantom{653}} 79\dfrac{7}{9}

(iii) 1112\dfrac{11}{12} 653\boxed{\phantom{653}} 1314\dfrac{13}{14}

Fractions

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Answer

(i) 56\dfrac{5}{6} and 1315\dfrac{13}{15}

By cross multiplication,

5 × 15 = 75 and 6 × 13 = 78.

Since 75 < 78, therefore, 56<1315\dfrac{5}{6} \lt \dfrac{13}{15}.

Hence, 56<1315\dfrac{5}{6} \lt \dfrac{13}{15}.

(ii) 45\dfrac{4}{5} and 79\dfrac{7}{9}

By cross multiplication,

4 × 9 = 36 and 5 × 7 = 35.

Since 36 > 35, therefore, 45>79\dfrac{4}{5} \gt \dfrac{7}{9}.

Hence, 45>79\dfrac{4}{5} \gt \dfrac{7}{9}.

(iii) 1112\dfrac{11}{12} and 1314\dfrac{13}{14}

By cross multiplication,

11 × 14 = 154 and 12 × 13 = 156.

Since 154 < 156, therefore, 1112<1314\dfrac{11}{12} \lt \dfrac{13}{14}.

Hence, 1112<1314\dfrac{11}{12} \lt \dfrac{13}{14}.

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