Subject Mathematics

Grade 5th

Students` Learning Outcomes

  • Add and subtract and more fractions with different denominators.

Information for Teachers

  • In the begging, numbers were counted in whole. Later on, to count the part of whole, the concept of fraction was given.
  • Fraction number has two parts. Upper part is called numerator and bottom part is called denominator.


  • Once you understand the concept of addition of fractions with different denominators, you can directly apply the addition process in following ways: (2 / 7 ) + ( 3 / 5 )
  • Find LCM of denominators and divide the LCM by denominator & multiply its quotient with respective numerators and we get: [( 2 x 5 ) + ( 3 x 7)/ 35]
  • Solve the Parenthesis and we get: = [10 + 21] / 35
  • Solve Braces and we get: = 31 / 35
  • Teacher should also consult with textbook at all steps where and when applicable.

Material / Resources

Writing board, chalk / marker, duster, textbook


  • Draw a square on board.
  • Divide the square into eight equal parts.
  • Colour in 4 parts.
  • Ask the students:

o   How many total parts of square? (8)

o   How many of these are coloured? (4)

o   Write it in fraction form. (4/8)

  • Tell the students that upper number is called numerator and bottom number is called denominator.


  • Write another fraction 2/5 on board.
  • Ask them: what is the denominator of this fraction?


o   Are the denominators of 4/8 and 2/5 same?

  • Tell them that those fractions which have same denominators are called like fractions and which have different denominators are called unlike fractions.


Activity 1

  • Draw the following figure on board and discuss with students about the like and unlike fractions and how to interchange between them.
  • On board discussion on “How to make equivalent fraction”?
  • (This will help in addition and subtraction)



Activity 2

  • Start the lesson by presenting a situation that involves the addition of fractions with unlike denominators and use student names from the class. For example, Bilal bought 5/6 of a kilogram of flour and Aliya bought ½ of a kilogram of flour. Record both fractions on the board.
  • Ask the students:

o   Which student bought more flour Bilal or Aliya?

o   Bilal and Aliya would like to calculate that how much flour they have altogether.

  • Does the situation call for addition, subtraction, multiplication or division? Why? Then ask students to estimate how much flour the two students purchased altogether / (plus) 5 / 6 + 1 / 2 = 5 + 3 / 6 = 8 / 6
  • Ask students how they might represent in figure A Bilal portion of flour, 5/6 of a kg. i
  • What could the whole box B represent? (One unit)
  • Draw a figure like this.


  • Ask students what each of these parts represents (1/6 of a kg)
  • How many parts could be coloured to represent Bilal share. (5)
  • Demonstrate by using different colour chalks if possible.



  • Draw another fraction box and repeat the process with a different color [if possible] to represent the amount of flour that Aliya bought.



  • Ask students to refine their original estimates based on the given figure.
  • Altogether, do you think they have less than 1 kg of flour, about 1 kg, more than 1 kilogram, or more than 2 kg?
  • How you might add Bilal`s and Alay’s portions of flour?
  • How can we add fractional amounts that are not the same size? Collect their responses, appreciate the closer one.
  • Can we find an equivalent fraction for ½, whose denominator would be “6”.
  • For example: 1 /2 of a kg is equivalent to 2/4 kg, but are Bilal`s and Alay’s pieces all the same size? Continue changing the denominator in the fraction until students see that 1 / 2 is also equivalent to 3/6, and that both Bilal`s and Alay’s portion can be thought of in terms of sixths.



  • Now that Bilal`s and Alay’s portion of flour are both in sixths of a kilogram, the pieces can be easily combined.
  • Draw fraction boxes to make 1 whole.



  • Ask students to determine, based on the model, how much flour Bilal and Aliya have altogether. 1, 2/6 or 8 / 6
  • At the end tell them that 5 / 6 + 3 / 6 = 1, 1 / 3


Activity 3

  • Write one fraction addition on board and ask them to solve. For example,   1 / 3 + 1 / 4  
  • Allocate time, move around the class and observe how do they attempt?
  • After this check the work of all students.
  • Finally ask any student to come on board and attempt that question.
  • Addition of Fractions:


  • When adding fractions you must have a common denominator
  • Write an example on the board: 3 / 6 + 1 / 5 =?
  • Say: Find the smallest number which is divided by 6 and 5 both. This number is 30. Then multiply both the numerator and denominator to get 30.
  • Once you have a common denominator, then add! (21 / 30)
  • Assign questions to the pairs.
  • Later give individual work.
  • Addition of Mixed Fractions:
  • Say: the rule is the same; you must have a common denominator to add fraction!
  • Write an example on the board, 6, 1 / 2 + 5, 1 / 3
  • Ask them, which are the whole number? (5, 6)
  • Ask them to add these whole numbers? (5 + 6 = 11)
  • Ask them to add fractions 1 / 2 and 1 / 3.
  • Say: once you have the common denominator, add the fractions, and then add the whole number separately.
  • Subtraction of Fractions:
  • To subtract fractions you must have a common denominator. For this purpose, subtract both numerators and write same denominator.


Sum up / Conclusion

  • With all these examples we have seen that for addition or subtraction of fractions we have to make the denominator alike.
  • So let`s wrap up the day, ask students to reflect back and recall all the examples done in the class.
  • To make denominator alike, we use making equivalent method, which we have already done in previous class.


  • Write down two questions on board:  1 / 2 + 4 / 7 and 3 / 5 – 2 / 6
  • Ask the students to solve these on their copies.
  • Round the class and assist them.

Follow up

  • If we have one-half orange and one-third orange then what will be the total of these?
  • If cut off one-fourth of one cake from three-fourth of that cake, then how much we have left?

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