MULTIPLYING FRACTIONS MADE EASY - LUCID EXPLANATION OF FRACTION PROBLEMS

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Please study
Fractions before Multiplying Fractions
if you have not already done so.

There we studied about half, quarter, three fourthwith examples and exercises.

Also study Fractions Made Easy.

There we studied about concept of fraction in generalwith examples and exercises.

The knowledge of

Equivalent Fractions

and

Conversion of Improper to Mixed and Mixed to Improper Fractions

is also used here.

Learn/Teach
Fractions through Fun Games.
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Here, we explain Multiplication of fractions,reciprocal or multiplicative inverse andUse of the operation 'of'in a lucid way. We include solved examples and problems for practice with answers.




Product of fractions = (Product of their numerators)⁄(Product of their denominators)

Thus,

ab xcd = (a x

c)⁄ (bx d)


Note : Every natural number is a fraction with denominator 1.
1 = 1⁄1; 2 = 2⁄1; 3 = 3⁄1; 4 = 4⁄1; etc.





Solved Example 1 of Multiplying Fractions

Find the value of

5  45 x 1  25 x7  34 x2  37 x 10⁄7

Solution :

5  45 x 1  25 x7  34 x2  37 x 10⁄17
= (5 x 5 + 4)⁄5 x (1 x 5 + 2)⁄5 x (7 x 4 + 3)⁄4x (2 x 7 + 3)⁄7 x 10⁄17
= 29⁄5 x 7⁄5 x 31⁄4 x 17⁄7 x 10⁄17

Here 17 and 7 in the Nr and Dr get cancelled.
These are shown by striking them off.
5 in the Dr goes 2 times in 10 in the Nr.
This is shown by striking 5 off
and writing 2 in the place of striked off 10.
This 2 in the place of 10 in Nr goes
2 times in the place of 4 in Dr.
These are again shown by striking off 2 in the Nr
and writing 2 in the place of striked off 4 in Dr.

= 29⁄5 x 75 x 31⁄42 x 177 x 10217
= 29⁄5 x 31⁄2 = (29 x 31 )⁄(5 x 2) = 899⁄10
= 89  910. Ans.

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Solved Example 2 of Multiplying Fractions

Find the value of
6 x 4  12 x 5  34 x9  12 xx 1⁄57

Solution :

6 x 4  12 x 5  34 x9  12 x1⁄57
= 6⁄1 x (4 x 2 + 1)⁄2 x (5 x 4 + 3)⁄4 x (9 x 2 + 1)⁄2x 1⁄57
= 6⁄1 x 9⁄2 x 23⁄4 x 19⁄2 x 1⁄57
= 63⁄1 x 9⁄2 x 23⁄4 x 192 x 1⁄573
= 9⁄2 x 23⁄4 = (9 x 23)⁄(2 x 4) = 207⁄8
= 25  78. Ans.

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Solved Example 3 of Multiplying Fractions

Find the value of
8 x 2  34 x 9  211 x2  67 x 1⁄120

Solution :

8 x 2  34 x 9  211 x2  67 x 1⁄120
= 8⁄1 x (2 x 4 + 3)⁄4 x (9 x 11 + 2)⁄11 x (2 x 7 + 6)⁄7x 1⁄120
= 8⁄1 x 11⁄4 x 101⁄11 x 20⁄7 x 1⁄120
= 82⁄1 x 114 x 101⁄11 x 20⁄7 x 1⁄12063
= 101⁄(7 x 3) = 101⁄21
= 4  1721. Ans.

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Reciprocal or Multiplicative Inverse of a Fraction : Multiplying Fractions

If two fractions are such that their product is 1, then each is called the reciprocal of the other.


Since ab xba = (a x

b)⁄ (bx a)=

1,so,

the reciprocal of abis ba.

Thus,

To write the reciprocal of a fraction, we interchangeits numerator and denominator.

Examples :

(i) reciprcal of 2⁄3 is 3⁄2.

(ii) reciprcal of 1⁄7 is 7⁄1.

(iii) reciprcal of 8 is 1⁄8.

(iv) reciprcal of 6  45
= reciprcal of (6 x 5 + 4)⁄5
= reciprcal of 34⁄5
= 5⁄34.

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Use of the operation 'of'

The operation 'of' is nothing but multiplication.

Examples :
(i) 1⁄2 of 8 = 8 x 1⁄2 = 4.;
(ii) 4⁄5 of 20 = 20 x 4⁄5 = 16.;

So, "fraction of a number " are
problems of Multiplying Fractions.

Word Problems on Multiplying Fractions

For Application of various topics of Fractionsincluding Multiplying Fractions to Word Problems go to

Fraction Word problems.

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Exercise on Multiplying Fractions

Solve the following problems on Multiplying Fractions.

  1. Find the value of
    4  56 x 1  57 x5⁄29 x 4
  2. Find the value of
    3  13 x 2  13 x6⁄7 x 2
  3. Find the value of
    3  14 x 2  16 x12⁄26
  4. Write the reciprocals of
    1. 8⁄9
    2. 1⁄13
    3. 14
    4. 2  34
  5. Find the values of
    1. 2⁄3 of 9
    2. 7⁄16 of 144
For Answers, see at the bottom of the page.

Answers to Exercise on Multiplying Fractions

Answers to Problems on Multiplying Fractions :

  1. 5  57
  2. 13  13
  3. 3  14
    1. 9⁄8
    2. 13
    3. 1⁄14
    4. 4⁄11
    1. 6
    2. 63