LESSON PLANNING OF DIVIDE A FRACTION BY ANOTHER FRACTION
Students` Learning Outcomes
- Divide a fraction by another fraction.(proper, improper and mixed)
o Solve real life problems related to division of fractions.
Information for Teacher
- Division of fractions is actually a continuous process of division of whole numbers.
- In proper fraction, denominator is always greater than numerator. So, proper fraction is always less than”1”.
- In improper fraction, denominator is always less than numerator. So, improper fraction is always greater than “1”.
- There is a whole number and one proper fraction in a mixed number.
- Approaches to division of fractions:
o Invert divisor and then multiply. 3 / 4 ÷ 5 / 7 = 3 / 4 x 7 / 5 = 21 / 20
o Divide numerator and denominator approach.
While teaching the lesson, the teacher should also consult with textbook where and when applicable.
Material / Resources
Writing board, chalk / marker, textbook
- Ask few multiplication table questions, 6 x 7? And 42 ÷ 6 =?
- Talk about relationship between multiplication and division leading to the conclusion that for each multiplication statement, two division statements may be written e.g. for 3 x 4 = 12, the corresponding division statements are 12 ÷ 4 = 3 and 12 ÷ 3 = 4.
- Ask students:
- What is a fraction, how you express it?
o Part of a whole.
o Locations on number lines.
o As division of whole numbers.
- Say statement before students “Save 1 / 2, 1 / 3, 1 / 4.
- Ask which one saving is more and why? Tell them: greater the denominator smaller the number.
- Say a statement:
- o On dividing one-half cake into one-fourth. How many pieces we get?
- Ask students to write down this statement into fractional form.
- Write down on the board with the help of student:
1 / 2 ÷ 1 / 4
- Tell them, it is the division of proper fractions.
- Tell that students that 15 / 5 means that find out how many groups of 5 in 15?
- Write a question on board:
1 / 2 ÷ 1 / 4
- Ask the students that what does mean by 1 / 2 ÷ 1 / 4 in the light of above mentioned concept?
- In case of getting no answers tell them that questions are that how many groups of 1 / 4 in 1 / 2?
- To develop this concept, take a paper and distribute it into 4 equal parts.
- Say to fill the colour in 1 / 4th part.
- Ask the students how many 1 / 4 will be fit into 1 / 2 of the same measurement paper, so 1 / 2 ÷ 1 / 4 = 2
- Now, tell the students direct method to solve the division of two fractions that we will take the reciprocal of denominator (1/4) which is (4 / 1) and convert the operation of division into multiplication, then on solving we get required answer.
- For practice write a question on board. Call any one student to solve this.
- Ask students:
o The number 2 1 / 2 isrelated to which type of fraction? (mixed fraction)
o How many whole and part in 1 ½? (2 whole and ½ part)
o How many whole and part in 1 ¼?
- Write a question on board: 2 ½ ÷ 1 ¼.
- Ask students that it is division of which type of fraction? (Mixed fraction)
- Ask them to convert these mixed fractions into improper fractions on their copies. (5 / 2 ÷ 5 / 4)
- Tell students that to solve this adopt the same process as given in activity 1.
- Similarly develop the concept of division of improper fraction into students.
- Say following statement:
- o If one-fourth of three-fourth of pizza is distributed among some people then it will be distributed in how many people?
- Ask the students that:
o How will write three-fourth in fraction? (3/4)
o How will write one-fourth in fraction? (1/4)
o How will write the whole given statement?
- Write on the board with the help of students: 3 / 4 ÷ 1 / 4
- Now, ask from anyone student that what will we do to solve it?
- If students provide answer then encourage them otherwise. Solve it with the help of students on board:
3 / 4 x 1 / 4 = 3 / 1 = 3
- Ask once again the said pizza will be distributed among how many people? (in 3 people)
Sum up / Conclusion
- Invert divisor and multiply; 3 / 4 ÷ 5 / 7 = 3 / 4 x 7 / 5 = 21 / 20
- Divide numerator and denominator approach; 6 / 25 ÷ 2/ 5 = 6/25 ÷ 2 / 5 = 3 / 5
- Ask student to solve the following questions on their copies:
- Round in class and assist them properly.
- Aslam has Rs. 40 ½. If he gave Rs.1 1/3 to each person how many person got the said amount.
- If 15 ¼ biscuits divided into five people, then how many biscuits will get each people?