# CLASS-5MULTIPLICATION OF FRACTION

Multiplication Of Fractions -

To use the method of cancellation to multiply two or more fractions first identify one numerator and one denominator in your problem that share a common factor. Then you cross out each one of those numbers and then you change it to however many times the common factor fits inside each number.

Numerators can only be cancelled with denominators. Two numerators or two denominators cannot be cancelled with each other.

Equal factors in the numerator and denominator can be cancelled with each other.

To multiply fractions, you need to follow these steps :-

1. Multiply the numerators (top numbers) together.
2. Multiply the denominators (bottom numbers) together.
3. Simplify the resulting fraction by reducing it to its lowest terms, if possible.

For example, let's say we want to multiply 2/3 and 4/5:

1. 2/3 x 4/5 = (2 x 4) / (3 x 5) = 8/15
2. We cannot simplify 8/15 any further, so that is our final answer.

So, 2/3 x 4/5 = 8/15.

Properties Of Multiplication -

1) Changing the order of the fractional numbers does not change the product.

[Example -

1          3          5              3           5            1

------ X ------ X ------- OR ------ X ------- X ------ OR

2          7          9              7           9            2

5           1            3

------- X ------- X ------- ]

9           2            7

2) The product of a fraction and 1 is the fraction itself

7               7

[Example:  ------ X 1 = ------- ]

8               8

3) The product of a fraction and 0 is 0

[Example:

3

------- X 0 = 0 ].

7

7

Example.1)  -------- X 3

9

7

------- X 3

9

7            3

=  ------- X --------

9            1

[dividing (numerator 3) and (denominator 9) by their common factor 3]

7

=  -------      (Ans.)

3

3             2

Example.2)   5 ------ X 2 -------

8             9

3            2

5 ------ X 2 -------

8             9

[Convert the mix fraction into improper fraction number]

(5 X 8) + 3          (2 X 9) + 2

= ------------- X --------------

8                    9

43           20

=  -------- X -------

8            9

[dividing (numerator 20) and (denominator 8) by their common factor 4]

43            5

=   -------- X -------

2            9

43 X 5

=  ------------

2 X 9

215

= --------

18

[Convert the improper fraction into mixed number]

17

=  11 --------             (Ans.)

18