Question

Arrange the following in descending order.
$\dfrac{5}{2},\dfrac{3}{2},\dfrac{7}{2},\dfrac{9}{5},\dfrac{9}{8}$

Answer 1

Hint: Take the L.C.M of denominators of all the given rational numbers. Multiply the numerator and denominator of each rational number by a specific number so that the denominator of each rational number provided, equals the L.C.M. Now, when the denominator of each fraction becomes the same, check the numerators of the obtained fractions. To write the fraction in descending order, arrange the fraction in order of having highest numerator to the fraction having lowest numerator.

Complete step-by-step answer:
We have been provided with the fractions: $\dfrac{5}{2},\dfrac{3}{2},\dfrac{7}{2},\dfrac{9}{5},\dfrac{9}{8}$. We have to arrange these fractions in descending order, that means, the fractions having highest value will be written first and the fraction having lowest value will be written at last.
In the above fractions, we can see that the first three are having the same denominators. Therefore they can be easily arranged in descending order. But the next two fractions are having different denominators, so it will be somewhat confusing to arrange them in the required order. So, first we must make the denominators of all the fractions equal.
Now, we know that the denominators are 2, 5 and 8. Therefore, their L.C.M will be 40. Now, we have to make the denominator of each fraction equal to 40. So, the various fractions can be written as:
$\begin{align}
  & (i)\text{ }\dfrac{5}{2}=\dfrac{5}{2}\times \dfrac{20}{20}=\dfrac{100}{40} \\
 & (ii)\text{ }\dfrac{3}{2}=\dfrac{3}{2}\times \dfrac{20}{20}=\dfrac{60}{40} \\
 & (iii)\text{ }\dfrac{7}{2}=\dfrac{7}{2}\times \dfrac{20}{20}=\dfrac{140}{40} \\
 & (iv)\text{ }\dfrac{9}{5}=\dfrac{9}{5}\times \dfrac{8}{8}=\dfrac{72}{40} \\
 & (v)\text{ }\dfrac{9}{8}=\dfrac{9}{8}\times \dfrac{5}{5}=\dfrac{45}{40} \\
\end{align}$
Now, since the denominator of each term is 0. Therefore, now we have to check the numerator.
Arranging the terms having numerator greatest to smallest, we have,
$\dfrac{140}{40},\dfrac{100}{40},\dfrac{72}{40},\dfrac{60}{40},\dfrac{45}{40}$
Now, equating their original form, we get,
\[\dfrac{7}{2},\dfrac{5}{2},\dfrac{9}{5},\dfrac{3}{2},\dfrac{9}{8}\]. Hence, this is the required descending order.

Note: If we will not make the denominators of all the fractions equal, then it will be difficult for us to arrange the given fractions in descending order. However, an alternate method can be applied to solve this question. We can convert the given fractions into decimals and then compare them. The decimal having highest value will be written first and the decimal having least value will be written at last.