MULTIPLYING FRACTIONS MADE EASY - LUCID EXPLANATION OF FRACTION PROBLEMS

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

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

Also study Fractions Made Easy.

There we studied about concept of fraction in general with 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.
For details, see near
the bottom of this page.

Here, we explain Multiplication of fractions, reciprocal or multiplicative inverse and Use 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)

a⁄b x c⁄d = (a x c) ⁄ (b x 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  ⁴⁄₅ x 1  ²⁄₅ x 7  ³⁄₄ x 2  ³⁄₇ x 10⁄7

Solution :

5  ⁴⁄₅ x 1  ²⁄₅ x 7  ³⁄₄ x 2  ³⁄₇ x 10⁄17
= (5 x 5 + 4)⁄5 x (1 x 5 + 2)⁄5 x (7 x 4 + 3)⁄4 x (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 7⁄5 x 31⁄4² x 17⁄7 x 10²⁄17
= 29⁄5 x 31⁄2 = (29 x 31 )⁄(5 x 2) = 899⁄10
= 89  ⁹⁄₁₀. Ans.

Solved Example 2 of Multiplying Fractions

Find the value of
6 x 4  ¹⁄₂ x 5  ³⁄₄ x 9  ¹⁄₂ x x 1⁄57

Solution :

6 x 4  ¹⁄₂ x 5  ³⁄₄ x 9  ¹⁄₂ x 1⁄57
= 6⁄1 x (4 x 2 + 1)⁄2 x (5 x 4 + 3)⁄4 x (9 x 2 + 1)⁄2 x 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 19⁄2 x 1⁄57³
= 9⁄2 x 23⁄4 = (9 x 23)⁄(2 x 4) = 207⁄8
= 25  ⁷⁄₈. Ans.

Solved Example 3 of Multiplying Fractions

Find the value of
8 x 2  ³⁄₄ x 9  ²⁄₁₁ x 2  ⁶⁄₇ x 1⁄120

Solution :

8 x 2  ³⁄₄ x 9  ²⁄₁₁ x 2  ⁶⁄₇ x 1⁄120
= 8⁄1 x (2 x 4 + 3)⁄4 x (9 x 11 + 2)⁄11 x (2 x 7 + 6)⁄7 x 1⁄120
= 8⁄1 x 11⁄4 x 101⁄11 x 20⁄7 x 1⁄120
= 8²⁄1 x 11⁄4 x 101⁄11 x 20⁄7 x 1⁄120⁶³
= 101⁄(7 x 3) = 101⁄21
= 4  ¹⁷⁄₂₁. Ans.

Reciprocal or Multiplicative Inverse of a Fraction

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

Since a⁄b x b⁄a = (a x b) ⁄ (b x a) = 1, so,

the reciprocal of a⁄b is b⁄a.

Thus,

To write the reciprocal of a fraction, we interchange its 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  ⁴⁄₅
= reciprcal of (6 x 5 + 4)⁄5
= reciprcal of 34⁄5
= 5⁄34.

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.;

Word Problems on Multiplying Fractions

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

Fraction Word problems.

Learning/Teaching Math Can Be Fun

Here is a collection of kids math
games and fun math activities for
the class room or for the home, to
make math exciting and easy to learn.

They help you

* To save you time and money to be
spent on resources, games and books.

* To become a wonderful, fun teacher
or parent who knows how to make math
fun, interesting and effective.

* To cater for all different ability
levels and cater for different
learning styles.

* To see your kids math skills soar
and their grades in math going
up and up.

This Collection of Fun Math Games
are electronic books (e-books)
that are downloaded to your computer
in a flash. You can start printing
games right away. You get to print
only what you want and as many
copies as you need.

For more information or to have
some FREE samples or to order
click HERE.

Exercise on Multiplying Fractions

1. Find the value of
   4  ⁵⁄₆ x 1  ⁵⁄₇ x 5⁄29 x 4
2. Find the value of
   3  ¹⁄₃ x 2  ¹⁄₃ x 6⁄7 x 2
3. Find the value of
   3  ¹⁄₄ x 2  ¹⁄₆ x 12⁄26
4. Write the reciprocals of
   1. 8⁄9
   2. 1⁄13
   3. 14
   4. 2  ³⁄₄
5. Find the values of
   
   1. 2⁄3 of 9
   2. 7⁄16 of 144

Answers to Exercise on Multiplying Fractions

Answers to Problems on Multiplying Fractions :

1. 5  ⁵⁄₇
2. 13  ¹⁄₃
3. 3  ¹⁄₄
4. 1. 9⁄8
   2. 13
   3. 1⁄14
   4. 4⁄11
5. 1. 6
   2. 63