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Q.

What is the correct arrangement of the fractions $\dfrac{5}{8}, \dfrac{7}{12}, \dfrac{13}{16}, \dfrac{16}{29}$ and $\dfrac{3}{4}$ in ascending order of magnitude.

 A.

$\dfrac{16}{29} < \dfrac{7}{12} < \dfrac{5}{8} < \dfrac{3}{4} < \dfrac{13}{16}$

 B.

$ \dfrac{16}{29} < \dfrac{7}{12} < \dfrac{5}{8} < \dfrac{13}{16} < \dfrac{3}{4} $

 C.

$\dfrac{7}{12} < \dfrac{16}{29} < \dfrac{5}{8} < \dfrac{13}{16}< \dfrac{3}{4}$

 D.

$\dfrac{16}{29} < \dfrac{5}{8} < \dfrac{7}{12} < \dfrac{3}{4} < \dfrac{13}{16}$

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Solution:
Option(A) is correct

Converting each of the given fractions into decimal form, we get :

$\dfrac{5}{8} = 0.624$

$\dfrac{7}{12} = 0.8125$

$\dfrac{16}{29} = 0.5517$,and

$\dfrac{3}{4} = 0.75$

Now, $0.5517 < 0.5833 < 0.625 < 0.75 < 0.8125$
⇒ $\dfrac{16}{29} < \dfrac{7}{12} < \dfrac{5}{8} < \dfrac{3}{4} < \dfrac{13}{16}$

Edit: For a different approach to solve this question, check comment by Rammy.


(1) Comment(s)


Rammy
 ()

Multiply the numerators with LCM of the denominators $(3x16x29)$. you will clearly see 4 fractions value of 5.

Arrange the 4 and you will get to the answer.

*do not simplify.