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Mathematics

Compare the following pairs of fractions:

(i) 59\dfrac{5}{9} and 45\dfrac{4}{5}

(ii) 916\dfrac{9}{16} and 59\dfrac{5}{9}

Fractions

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Answer

(i) 59\dfrac{5}{9} and 45\dfrac{4}{5}

LCM of 9 and 5 = 45.

Write the given fractions as equivalent like fractions.

59=5×59×5=254545=4×95×9=3645\Rightarrow \dfrac{5}{9} = \dfrac{5 \times 5}{9 \times 5} = \dfrac{25}{45} \\[1em] \Rightarrow \dfrac{4}{5} = \dfrac{4 \times 9}{5 \times 9} = \dfrac{36}{45}

As 25 < 36, 2545<364559<45\dfrac{25}{45} \lt \dfrac{36}{45} \Rightarrow \dfrac{5}{9} \lt \dfrac{4}{5}.

Hence, 59<45\dfrac{5}{9} \lt \dfrac{4}{5}.

(ii) 916\dfrac{9}{16} and 59\dfrac{5}{9}

LCM of 16 and 9 = 144.

Write the given fractions as equivalent like fractions.

916=9×916×9=8114459=5×169×16=80144\Rightarrow \dfrac{9}{16} = \dfrac{9 \times 9}{16 \times 9} = \dfrac{81}{144} \\[1em] \Rightarrow \dfrac{5}{9} = \dfrac{5 \times 16}{9 \times 16} = \dfrac{80}{144}

As 81 > 80, 81144>80144916>59\dfrac{81}{144} \gt \dfrac{80}{144} \Rightarrow \dfrac{9}{16} \gt \dfrac{5}{9}.

Hence, 916>59\dfrac{9}{16} \gt \dfrac{5}{9}.

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