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Comparing and Ordering Fractions

Comparing fractions can be done in many ways. Here students will learn how to compare fractions.

In this learning concept, the students will learn to

  • Classify by comparing unlike fractions and comparing like fractions.
  • Identify ascending and descending order in fractions.
  • Evaluate the arranging fraction in ascending order.

 

Each concept is explained to class 5 maths students using illustrations, examples, and mind maps. Students can assess their learning by solving the two printable comparing fractions worksheets given at the page’s end.

Download the comparing fractions worksheet for class 5 and check the solutions for the comparing fractions provided in PDF format.

We can categorise all fractions into two types:

       1.Like fractions: Fractions that have same denominators.

          2/7, 5/7, 6/7, etc

      2. Unlike fractions: Fractions that have different denominators.

         3/5, 3/7, 4/9, etc

Comparison of fractions can be done in the following categories.

  1. Comparing like fractions
  2. Comparing unlike fraction             

              a. Comparing unlike fractions with same numerators

              b. Comparing unlike fractions with different numerators

     1. Comparing Like Fractions

          Example 1: Let’s take an example of like fractions.

         3/4, 1/4, → Like fraction

          Like fractions

         Compare the numerators.

         3 > 1

         So,

          Like fractions


       Example 2:

       6/12, 11/12, → Like fraction

       Like fractions
    

      Compare the numerators.

      6 < 11

      so, 6/12 is smaller than 11/12.

      Like fractions

      From the above example:

      G5_5_Comparing and Ordering Fraction_Note box

 

      2. Comparing Unlike Fractions

              a. Comparing Unlike Fractions With the Same Numerators

                   Example 1: Let’s take an example of unlike fractions with same numerator.

                   1/2 and 1/8

                    Unlike fractions

                   Compare the denominators.

                   2 < 8.

                   The fraction with the smaller denominator is the greater. So,

                    Unlike fractions

                    G5_8_Comparing and Ordering Fraction_Note box

              b. Comparing Unlike Fractions With Different Numerators

                  Example : Let’s take an example of unlike fractions with different numerator.

                  1/3 and 3/8

                  Unlike fractions
                Here, we cannot predict which portion is larger and which one is smaller.

               G5_10_Comparing and Ordering Frcation_Box
              Step 1: LCM of 3 and 8.

              3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ......

              8 = 8, 16, 24, 32, .....

             So, LCM of 3 and 8 is 24.

             Step 2: Find equivalent fractions.

            (Multiply numerator and denominator by the same number so that denominator will be 24.)

            1/3 = 1 x 8/3 x 8 = 8/24
            3/8 = 3 x 3/8 x 3 = 9/24

            Like fractions

            8 < 9

            So, 8/24< 9/24

            Like fractions

            So, 1/3< 3/8

           Comparing Fractions

                                                                                                 Ordering Fractions

  • Ordering Like Fractions

         Example : Arrange the following fractions in Ascending order and descending order.

         7/13, 9/13, 12/13

         Ascending Order in Fraction:

    • If denominators of the fractions are the same, arrange fractions according to ascending order of the numerators.
    • The fraction which has the smallest numerator is the smallest fraction among all. So, ascending order of the fraction is:
                  5/13, 7/13 , 9/13, 12/13

        Descending Order in Fraction:

    • If denominators of the fractions are the same, arrange fractions according to descending order of the numerators.
    • The fraction which has the biggest numerator is the biggest fraction among all. So, descending order of the fraction is:

                 12/13, 9/13, 7/13, 5/13

  •  Ordering Unlike Fractions

          Case 1: Numerators are same

          Example : Arrange the following fractions in Ascending order and descending order.

         17/3, 17/11, 17/9, 17/15

          Ascending Order in Fraction:

    • If numerators of the fractions are same, arrange fractions according to descending order of the denominators.
    • The fraction which has the biggest denominator is the smallest fraction among all. So, ascending order of the fraction is: 
                  17/15, 17/11, 17/9, 17/3

         Descending Order in Fraction:

    • If numerators of the fractions are the same, arrange fractions according to ascending order of the numerators.
    • The fraction which has the smallest denominator is the biggest fraction among all. So, descending order of the fraction is:
                  17/3, 17/9, 17/11, 17/15

        Case 2: Numerators are different

        Example : Arrange the following fractions in Ascending order and descending order.

        3/4, 1/2, 7/12, 4/6

        Step 1:Find the LCM of denominators.

       Step 2:Make all denominators equal to LCM. It will convert all fractions into like fractions.

       Step 3:By using like fractions comparison rule, ordered the fractions.

       LCM of 4, 2, 12, 6 = 12

       3/4 = 3 x 3/4 x 3 = 9/12
       1/2 = 1 x 6/2 x 6 = 6/12
       7/12(Keep it as it is)
       4/6 = 4 x 2/6 x 2 = 8/12
       Now, we have new fractions: 9/12, 6/12, 7/12, 8/12
       Ascending order: 6/12, 7/12, 8/12, 9/12 = 1/2, 7/12, 4/6, 3/4 (Original fractions are equivalent to new fractions)
       Descending order: 3/4, 4/6, 7/12, 1/2

                                               Comparing and Ordering Fractions on a Number Line

     Number line: A number line is a straight line on which the numbers are placed at equal distances.

    Number line
   How to Write the Fractions on a Number Line?
  1. Write the Proper Fractions on a Number Line::
    • Step 1:Divide the interval from 0 to 1 into equal parts as equal to the denominator.
    • Step 2:Count the number of intervals from 0 as equal to the numerator. And make a mark.

                  Example

                  Write the fraction 4/5 on the number line.

                  Step 1:Divide the interval from 0 to 1 into 5 equal parts.

                  Step 2:Count 4 intervals from 0 and make a mark at the 4th interval.

                 The fraction 4/5 on a number line:

                   Number line

     2. Write the Improper Fractions on a Number Line:

    • Step 1:Convert the improper fraction into a proper fraction.
    • Step 2:Divide each interval into equal parts as many as the denominator.
    • Step 3:Count the number of intervals as equal to the numerator after the whole number of the mixed fraction.

                  Example

                  Write the fraction 5/3 on the number line.

                  Step 1:Convert the improper fraction 5/3 into a proper fraction.

                   Division

                 5/3 = 1 2/3

                Step 2:Denominator = 3

                Divide each interval into 3 equal parts.

               Step 3:Numerator = 2, whole number in mixed fraction = 1

               Count 2 intervals after 1.

               The fraction 1 2/3 = 5/3 on a number line:

                  Number line

              In this way, we can write any fraction on a number line.

     How to Compare and Order the Fractions by a Number Line?
  • Step 1: Make all the fractions like fractions.
  • Step 2: Write all the fractions on a number line.
  • Step 3: From left to right, all fractions are getting arranged in ascending order on a number line. Now compare all fractions.

         Example

         Compare the following fractions by using a number line and order them in ascending and descending order.

         1/2, 7/3 , 5/6
         Step 1: Make all the fractions like fractions.
         1 x 3/2 x 3 = 3/6
         7 x 2/3 x 2 = 14/6
         Division
       7/3 = 2 2/6

      Step 2:Write all the following fractions on a number line -

      3/6 = 1/2, 2 2/6 = 7/3, 5/6
        Number line

      Step 3:From left to right, all fractions are getting arranged in ascending order on a number line.

     So, the ascending order of the fraction: 1/2, 5/6, 7/3

     The descending order of the fraction: 7/3, 5/6, 1/2

 Misconception:

 Don’t be confused while comparing fractions with the same numerator.

 Example:

        comparing fractions

In the above example, numerators are same in both the fractions. Although the denominator of the first fraction is larger, that fraction is smaller. So, be careful when comparing fractions with equal numerators.

Did you know?

did you know for comparing fractions

 

Mind map of comparing fractions
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