Question

Arrange the following numbers in descending order.
\[ - 2,\dfrac{4}{{ - 5}},\dfrac{{ - 11}}{{20}},\dfrac{3}{4}\]

Answer 1

Hint: Descending order means arranging the numbers from the largest to the smallest. First, express the numbers such that they all have a common denominator by using LCM and then arrange them from the largest number to the smallest number.

Complete step-by-step answer:
Arranging the numbers from the largest value to the smallest value is called the descending order. For example, the descending order of numbers 0, 2, 1 is 2, 1, 0.
For integers, it is easy to arrange them from the largest number to the smallest number but for fractions, it is not straightforward.
First, we need to convert all the fractions such that they have a common denominator.
To get the common denominator, we find the LCM of the numbers in the denominator.
The numbers are 1, 5, 4, and 20. We know that the LCM of 1, 5, 4, and 20 is 20. Now, we convert the fractions.
The first number is – 2, we multiply numerator and denominator by 20 to get as follows:
\[ - 2 \times \dfrac{{20}}{{20}} = - \dfrac{{40}}{{20}}\]
The second number is \[ - \dfrac{4}{5}\], we multiply numerator and denominator by 4 to get as follows:
\[ - \dfrac{4}{5} \times \dfrac{4}{4} = - \dfrac{{16}}{{20}}\]
The third number is \[ - \dfrac{{11}}{{20}}\], the denominator is already 20, so we don’t disturb this number.
The fourth number is \[\dfrac{3}{4}\], we multiply numerator and denominator by 5 to get as follows:
\[\dfrac{3}{4} \times \dfrac{5}{5} = \dfrac{{15}}{{20}}\]
Now, we have the numbers as follows:
\[ - \dfrac{{40}}{{20}}, - \dfrac{{16}}{{20}}, - \dfrac{{11}}{{20}},\dfrac{{15}}{{20}}\]
Now, we can compare them as follows:
\[\dfrac{{15}}{{20}} > - \dfrac{{11}}{{20}} > - \dfrac{{16}}{{20}} > - \dfrac{{40}}{{20}}\]
Hence, the descending order is as follows:
\[\dfrac{3}{4},\dfrac{{ - 11}}{{20}},\dfrac{5}{{ - 5}}, - 2\]

Note: You can also divide the numbers and obtain the expression in the form of decimals and then compare the numbers to arrange them in descending order. Students should know that while determining the largest number from numbers having negative sign, the least value with negative sign gives the largest number.For ex. From -31 and -11 the largest number will be the least value with negative sign i.e -11 is the largest number.