Properties of Multiplication of Fractions.

PROPERTIES OF MULTIPLICATION OF FRACTIONAL NUMBERS:

The properties of multiplication of Whole numbers apply to the multiplication of Fractions as well.

 

1) The product of a Fraction and Zero is Zero.

    2/3  x  0  =   0;   3 5/4  x  0  =  0.

 

2) The product of a Fraction and One(1) is the Fraction itself.

     3/8  x 1 = 3/8;   4 7/3 x 1 = 4 7/3.

 

3) Two fraction can be multiplied in any order, the product remains the same.

    1/6 x  2/7 =  (1x2) / (6x7)  = 2/42  ;  2/7 x 1/6 = (2x1)/(7x6) = 2/42.

 

4) While multiplying more than two fractions, they can be grouped in any order. The product remains the same.

Let the fractions be:  2/5 x 1/7 x 2/3

2/5 x (1/7 x 2/3) = (2x1x2) / (5x7x3) = 4/105.

                    (or)                                                           

(2/5 x 1/7) x 2/3 = (2x1x2) / (5x7x3) = 4/105.

                   (or)

(2/5 x 2/3) x 1/7 = (2x2x1) / (5x3x7) = 4/105.

Therefore, 2/5 x (1/7 x 2/3) = (2/5 x 1/7) x 2/3 = (2/5 x 2/3) x 1/7 = 4/105.

 

Fill in the blanks using Multiplication Properties:

1) 3/8 x 6/7 =  6/7 x 3/8.

2) (1/5 x 4/6) x 2/9 =  1/5 x  (4/6 x 2/9).

3) 5/9 x 0 = 0.

4) 5/7 x 1 = 5/7.  

5) 3/7 x 2/7 = 2/7 x 3/7.

6)  6/5 x (3/7 x 4/5) = (6/5 x 3/7) x 4/5.    

Properties of Division of Fractions.

PROPERTIES OF DIVISION OF FRACTIONS:

 1) When a fraction is divided by 1, the quotient is the fraction itself.

   2/5 ÷  1 = 2/5 ;    3/7 ÷ 1 = 3/7 ;   2  3/5  ÷ 1 =  2 3/5.

 

2) When Zero is divided by a fraction, the quotient is always Zero.

  0 ÷ 2/5  =  0 ;   0 ÷ 3 4/5 =  0 ;   0 ÷ 3/8  =  0.

Note: We cannot divide a fraction by Zero.

 

3) When a fraction is divided by itself, the quotient is One (1).

  2/5 ÷ 2/5 = 1 ;   3 4/5 ÷ 3 4/5 = 1  ;  3/7 ÷ 3/7 = 1.

 

Fill in the blanks using properties of division:

1)  4/7 ÷ 4/7 = 1 

2)  3/8 ÷ 1 = 3/8.

3) 4/9 ÷  4/9 = 1.

4) 0 ÷ 5/9 = 0.

5) 0 ÷ 2/9 = 0.