# MULTIPLICATION OF FRACTIONS

LESSON PLANNING OF MULTIPLICATION OF FRACTIONS

Subject Mathematics

Students` Learning Outcomes

• Multiply a fraction by a number and explain with the help of diagram.
• The students will be able to:
• o   Multiply a fraction by another fraction.
• o   Multiply two or more fractions involving brackets. (proper, improper and mixed fractions)
• o   Solve real life problems related to multiplication of fractions.

Information for Teachers

• Because of the order of operations, mixed numbers can`t be multiplied as it is. The method of multiplication is as under:

Three Step Method:

§  Change mixed numbers to improper or proper fractions.

§  Multiply numerators with numerators and denominator’s with dominators.

Simplifying Fractions:

§  Look at the numerators and denominators.

§  Decide if there are any common factors, or numbers that you can evenly divide into both the numerator and denominators. For example, in 3 / 4 x 2 / 1, 2 and the 4 have a common factor of 2.

§  Divide the numerator and denominator or you have chosen by the common factor in the example, you will have 3 / 2 x 1 / 1. On your paper you will cross out the number you have and put the new number that you get when you divide by the common factor.

§  Multiply numerators together and multiply denominators.

§  Teacher should also consult textbook where and when required.

Material / Resources

Writing board, chalk / marker, duster, textbook

Introduction

• Do you remember cancelling process? (Reducing before multiplying is called cancelling)

4 / 8 x 6 / 12, 3 / 4 x 12, 8 / 4 x 6, 3 / 7 x 14

• Allocate time for individual work.
• Do the same question on board with the help of the whole class.
• Announce that today we will explore about multiplying factions.

Development

Activity 1

• Ask, “Do you remember what we did in last class? “Multiplying a fraction by a number) e.g. 4 x 2 / 3
• Repeat that here the denominator of number “4” is “1”. Thus, multiply numerators with numerators and denominator with denominator. We get 8 / 3.
• Let`s try to draw some figures for multiplication of fractions.
• How represent fraction 1, 1/2 / 3 / 4 / in figures?

• Call volunteer to make figure on board.
• We can illustrate the multiplication problem above by picturing each fraction as part of a whole or unit. With that idea in mind, we can show the fraction as; 2 / 3 and 4 / 5

• Like in above example, we wanted to find 2 / 3 of 4 / 5. The “of” in this expression indicates that we are taking a part of something. That`s what multiplying fractions is really all about.

2 / 3 x 4 / 5 means 2 / 3 of a group of 4/ 5;

b)      Find 2 / 3 of 4 / 5 by drawing 3 equal rows across the shaded parts;

c)       Extend the horizontal cuts to determine how many equal pieces out of the whole are in the double-shaded region.  Therefore, 2 / 3 x 4 / 5 = 8 / 15

o   Did you also notice that the double shaded area is less than both fractions, 2 / 3 and 4 / 5 ? that`s because multiplying proper fractions always produces a smaller fraction.

o   Think about that for a moment. When we multiply a fraction by a fraction, aren`t we actually taking a “part” of a “part”?

o   As always, don`t forget to reduce or simplify your answer, as needed.

o   Remember to present your solution in the form asked for in your instructions. If you are asked to give answer in mixed or proper or improper fraction.

o   Once students understand the meaning & pictorial representation, tell them that now it`s their turn.

Activity 2

• For most students multiplying fractions is the easiest of the four basic operations. Do you know why?
• You don`t have to worry about a common denominator.

Here`s the Rule:

• o   Multiply the numerators.
• o   Multiply the denominators.
• o   Simplify or reduce the resulting fractions, if possible. [You may simplify first and then multiply, choice is yours!] 2 / 3 x 4 / 5 = (2 x 4) / (3 x 5) = 8 / 15

Activity 3

• Tell the students that if multiplication of fraction is given within the “Brackets” then order to solve these will be as under:

o   First of all small brackets       ( )

o   Then curly brackets                { }

o   And at end, square brackets [ ]

• Write a question on board:  [1 / 2 x {1 / 3 x (1 / 4 x 1 / 5)}]
• Call any one student on board and ask that which one part of question will solve firstly.
• After pointing out that part, say to solve that part and write the answer.
• Simplify (1 / 4 x 1 / 5) = 1 / 20
• Now, call another student on board and ask that now which one bracket will solve and how?
• Put 1 / 20 in place of (1 / 4 x 1 / 5), you get {1 / 3 x 1 / 20} = 1 / 60.
• And at the end, call another student on board and ask which one bracket will solve and how?
• Put 1 / 60 in place of {1 / 3 x (1 / 4 x 1 / 5)}, you get [1 / 2 x 1 / 60] = 1 / 120

Activity 4

5 days are what part of April?

Think over them that there are 30 days in April. Guide them towards required answer, as; 5 / 30 = 1 / 6 (one sixth)

Ask them, if you’re slept 8 hours at night then how much hours of a day you slept? (8 / 24) = 1 / 3

Make the proper groups of students and ask that if one fourth of a half cake is given to brother, then how much given to him.

Provide opportunity them to discuss and think within the groups. Guide them properly.

Tell them that actually we want to find the 1 / 4th of 1 / 2.

Now tell them that the meaning of word “of” is multiplication.

Now ask anyone student of a group to solve on the board, as;

o   One-half                              =  1 / 2

o   Of                                         = Multiplication

o   One-fourth                         = 1 / 4

o   One –fourth of one –half = 1 / 4 x 1 / 2 = 1 / 8

Sum up / Conclusion

• Multiplying proper fractions always produces a smaller fraction.
• For the multiplication of fractions, multiply numerators multiply denominator and then simplify the fractions.
• We can do cancellation or reducing to simplest terms.

To reduce a fraction, these steps are followed:

o   Factoring the numerator

o   Factoring the denominator

o   Cancelling out fraction mixes that have a value of 1.

Assessment

• Individual assignments:
• Write the following questions on the board and ask them to solve individually:

o   3, 2 / 5 x 1, 5 / 8 =

o   1, 2 / 5 x 7 =

o   [ 1 / 4 x ( 1 / 2 x ( 1 / 5 x 1 / 2)}]

Collect note books to check them later.

Give some questions from the textbook as well.

Teacher has contributed to solve the exercise question at the end of textbook.