Question

Arrange the following numbers in descending order:
 $ \dfrac{2}{3},\,\dfrac{3}{5},\,\dfrac{7}{{10}},\,\dfrac{8}{{15}} $

Answer 1

Hint: The arrangement of a set of numbers from highest to lowest is called the descending order. But the given numbers are fractions so to compare the numbers with each other, we have to find the LCM of the denominators and express them in such a way that they all have a common denominator.

Complete step-by-step answer:
As the name suggests, descending means moving from large to small thus descending order is the arrangement of numbers from largest to smallest. For example the descending order of the numbers 7, 10, -3 is 10, 7, -3.
The least common multiple of 3, 5, 10 and 15 is 30. So to convert the numbers into having common denominators, we have to multiply both the numerator and denominator by the same number.
The first number is $ \dfrac{2}{3} $ , we multiply the numerator and denominator with $ 10 $ and get –
 $ \Rightarrow \dfrac{2}{3} \times \dfrac{{10}}{{10}} = \dfrac{{20}}{{30}} $
The second number is $ \dfrac{3}{5} $ , we multiply the numerator and denominator with 6 and get –
 $\Rightarrow \dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{{18}}{{30}} $
The third number is $ \dfrac{7}{{10}} $ , we multiply the numerator and denominator with 3 and get –
 $\Rightarrow \dfrac{7}{{10}} \times \dfrac{3}{3} = \dfrac{{21}}{{30}} $
The fourth number is $ \dfrac{8}{{15}} $ , we multiply the numerator and denominator with 2 and get –
 $\Rightarrow \dfrac{8}{{15}} \times \dfrac{2}{2} = \dfrac{{16}}{{30}} $
Now, the numbers are obtained as follows –
 $ \dfrac{{20}}{{30}},\,\dfrac{{18}}{{30}},\,\dfrac{{21}}{{30}},\,\dfrac{{16}}{{30}} $
On comparing these numbers we get –
 $\Rightarrow \dfrac{{21}}{{30}} > \dfrac{{20}}{{30}} > \dfrac{{18}}{{30}} > \dfrac{{16}}{{30}} $
That is $ \dfrac{7}{{10}} > \dfrac{2}{3} > \dfrac{3}{5} > \dfrac{8}{{15}} $
Thus the descending order is $ \dfrac{7}{{10}},\,\dfrac{2}{3},\,\dfrac{3}{5},\,\dfrac{8}{{15}} $ .
So, the correct answer is “$ \dfrac{7}{{10}},\,\dfrac{2}{3},\,\dfrac{3}{5},\,\dfrac{8}{{15}} $ ”.

Note: Instead of finding the LCM and converting the numbers in such a way that they have a common denominator, we can also divide the two numbers and compare them in the decimal form. The least common multiple of a set of numbers is defined as the smallest possible number that is divisible by all the numbers in that set.