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Which of the following fractions \(\dfrac{3}{8},\dfrac{4}{5},\dfrac{31}{40},\dfrac{9}{20},\dfrac{7}{10}\) is greater than \(\dfrac{1}{2}\) and less than \(\dfrac{3}{4}\) ?


1. \(\dfrac{31}{40}\)
2. \(\dfrac{9}{20}\)
3. \(\dfrac{4}{5}\)
4. \(\dfrac{7}{10}\)

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Best answer
Correct Answer - Option 4 : \(\dfrac{7}{10}\)

Given:

\(\dfrac{3}{8},\dfrac{4}{5},\dfrac{31}{40},\dfrac{9}{20},\dfrac{7}{10}\)

Range = \(\left(\dfrac{1}{2} \right)\) to \(\left(\dfrac{3}{4}\right)\) 

Calculations:

Taking the LCM of denominators of all the term,

LCM of (8, 5, 40, 20, 10, 4, 2) = 40

Fractions with 40 as denominators are,

\(\dfrac{15}{40},\dfrac{32}{40},\dfrac{31}{40},\dfrac{18}{40},\dfrac{28}{40}\)

Range with 40 as denominators are,

\(\dfrac{20}{40} \) to \(\dfrac{30}{40} \)

The fraction that lies within the range is \(\dfrac{28}{40} \)

∴ The fraction that lies within the given range is \(\dfrac{7}{10}\)

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