# DIVIDE A FRACTION BY ANOTHER FRACTION

LESSON PLANNING OF DIVIDE A FRACTION BY ANOTHER FRACTION

Subject Mathematics

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

Introduction

• 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.
• 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.

Development

Activity 1

• 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.

Activity 2

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.

Activity 3

• 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?

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

Assessment

• Ask student to solve the following questions on their copies:

• Round in class and assist them properly.