Multiplying a fraction by a whole number

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Multiplication of a Fraction by a Whole number
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Observe the figures and think of the following
questions 2 minutes

• How much is represented in figure 1?
• In how many parts the whole apple is
• divided into? What is the relationship
• between the whole and the parts?
• 3. How many halves can you find in
• figure 3?

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Multiplication of Fraction by a Whole number
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• Objective of the lesson
• To multiply a fraction by a whole number
• Keywords
• Fraction, Multiply, Whole number, Product

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Read the following question

• If you have 8 of the half apples, in total, how
  many whole apples do you have? Think carefully
  and try to find out.

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So, 8 times ½ 4. Also, ½ x 8 4.
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Lets discuss the solution

• 8 times half means we can add halves eight times
  i.e. 1 2 s 8 times.
• So we get 1 2 1 2 1 2 1 2 1
  2 1 2 1 2 1 2
• which we can easily calculate by adding the like
  fractions
• and we get 8 2 4
• Now let's present this scenario in different
  form
• 8 times 1 2 means 8 x 1 2 .
• 8 is a whole number and we can consider 1 as its
  denominator.
• Now we can consider as the product of two
  fractions (in fact 8 is a whole number and every
  whole number can be considered as a fraction
  having denominator 1) and the rule is that in we
  multiply numerators together and denominators
  together.
• Then we reduce the fraction to the lowest form.

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An illustration
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An illustration
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The Rule!

• To multiply a fraction by a whole number,
• Multiply by the numerator and then divide by the
  denominator
• Example Multiply 3 5 x 4 3 ?? 4 5 12
  5 2 2 5

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Multiplying fractions by integers

• Example
• Multiply 4 9 by 54.

Rule Multiply by the numerator and divide by
the denominator
This is equivalent to 4 9 of 54.
54 9 4
6 4
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Multiplying fractions by integers

• What is 12 x 5 7

12 x 5 7
60 7
8 4 7
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The Extended Rule !

• To multiply a fraction by a whole number,
  multiply the numerator of the fraction by the
  whole number and write the product as the
  numerator over the denominator, if possible
  simplify.
• We can cancel a number in the numerator and a
  number in the denominator by a same factor as
  many times as possible.
• When there is no common factor between the
  numbers in numerator and denominator then we say
  that the fraction is in the lowest or the
  simplified form.
• Before multiplying the fraction by the whole
  number, you can first cancel or divide the
  denominator of the fraction against the whole
  number if cancellable.)

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• What is 16 x 7 12 ?

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28

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An Example

• What is 8 25 x 40 ?

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Classwork
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Plenary

• Discuss on why can we write a product as repeated
  addition and when might we not want to use
  repeated addition to find a product?
• Also Recall the rule for multiplying a fraction
  by a whole number.

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Homework

• Make a model for 3 5 x 6 and calculate the
  answer.

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