Question

How to arrange fractions in ascending and descending order?

Answer 1

Hint: We can solve this type of question in two ways. First way is that we have to check the denominator of all fractions, if they are equal we will compare the numerator and arrange them and the second way is that we can convert the given fractions into decimals and then compare and arrange them.

Complete step-by-step answer:
First way:
In this first way we will check the denominators of all the given fractions. If all the denominators are equal then simply compare the numerator and arrange fractions according to it. But if the denominators are not equal then take the LCM of all the denominators and make all denominators equal after that check the numerator and then arrange them in ascending order (from smaller to bigger number) or descending order(from bigger to smaller number).
Let’s understand this by taking an example-
Arrange the following fractions in ascending order:
 \[\dfrac{2}{3},\dfrac{1}{2},\dfrac{5}{6}\]
As we can see, denominators of given functions are not equal. So we have to take the LCM.
For LCM we have to find the lowest common multiples of \[3,2,6\] . So LCM of \[3,2,6\] is \[6\] (as it is the least common multiple in three of them).
Now making denominators equal:
 \[\Rightarrow \dfrac{2}{3}\times \dfrac{1}{2},\dfrac{1}{2}\times \dfrac{1}{3},\dfrac{5}{6}\times \dfrac{1}{1}\]
 \[\Rightarrow \dfrac{2}{6},\dfrac{1}{6},\dfrac{5}{6}\]
Now, all the denominators are equal and now we will check the numerator and arrange all the fractions on the basis of their numerators in ascending order:
 \[\Rightarrow \dfrac{1}{6}<\dfrac{2}{6}<\dfrac{5}{6}\]
As we can see that the given fractions have been arranged in the ascending order.

Second way:
In this, we will convert all the given fractions into the decimal and then we will compare all the decimals and then arrange them in ascending order (smaller number to bigger number) or descending order (bigger number to smaller number) as per our requirement.
Let’s understand this by taking an example-
Arrange the following given fractions in ascending order:
 \[\dfrac{3}{4},\dfrac{1}{2},\dfrac{4}{5},\dfrac{3}{8}\]
Now we will convert all the given fractions in decimal:
 \[\dfrac{3}{4}=0.75\]
 \[\dfrac{1}{2}=0.5\]
 \[\dfrac{4}{5}=0.8\]
 \[\dfrac{3}{8}=0.37\]
As we can see they all have \[0\] in their unit’s digit, therefore we will check and compare by the tenth digit and arrange them in ascending order.
 \[\Rightarrow 0.8<0.75<0.5<0.37\]
Now we can write their respective fractions:
 \[\Rightarrow \dfrac{4}{5}<\dfrac{3}{4}<\dfrac{1}{2}<\dfrac{3}{8}\]
And for descending order we can do the arrangement and vice versa.

Note: The word fraction originated from the Latin word “Fraction” which means breaking. There are basically six types of fractions- proper fraction, improper fraction, like fraction, unlike fraction, mixed fraction and equivalent fraction.Improper fraction can be converted into proper fraction just by dividing it.