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Mathematics

Identify a rational number between 13 and 45\dfrac{1}{3} \text{ and } \dfrac{4}{5}.

  1. 14\dfrac{1}{4}

  2. 910\dfrac{9}{10}

  3. 1730\dfrac{17}{30}

  4. 17101\dfrac{7}{10}

Rational Numbers

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Answer

Write the given rational numbers with the LCM of their denominators as the common denominator and compare them with the given options.

[ LCM of 3 and 5=30]⇒13=1×103×10=1030⇒45=4×65×6=2430[\text{ LCM of } 3 \text{ and } 5 = 30] \\[1em] \Rightarrow \dfrac{1}{3} = \dfrac{1 \times 10}{3 \times 10} = \dfrac{10}{30} \\[1em] \Rightarrow \dfrac{4}{5} = \dfrac{4 \times 6}{5 \times 6} = \dfrac{24}{30}

As 10 < 17 < 24, so 1030<1730<2430\dfrac{10}{30} \lt \dfrac{17}{30} \lt \dfrac{24}{30}

Hence, Option 3 is the correct option.

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