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.

Division of a Fractional number by a Whole number.

DIVISION OF A FRACTION BY A WHOLE NUMBER:

Steps to find Division of fraction by a whole number:

i) Find out the reciprocal of the Whole number.

ii) Multiply the Fraction with reciprocal of the Whole number.

iii) Simplify into its lowest terms.

Required Answer = Fraction x Reciprocal of the Whole number.

 

Solve the Following:

1) 5/9 ÷  4

Solution :

Given: Fraction = 5/9 ; Whole number = 4.

i) Reciprocal of the Whole number = 1/4

Required Answer =  Fraction x Reciprocal of the Whole number

                             =  (5/9)  x  (1/4) =  5/36.           

                                                                                   

2) 5/6 ÷ 4

Solution:

Given: Fraction = 5/6 ; Whole number = 4.

Reciprocal of the Whole number = 1/4

Required Answer =  Fraction x Reciprocal of the Whole number

                             =  (5/6) x (1/4) =  5/24.

 

3) 3/7 ÷ 3

Solution:

Given: Fraction = 3/7 ; Whole number = 3.

Reciprocal of the Whole number = 1/3.

Required Answer =  Fraction x Reciprocal of the Whole number

                             =  (3/7) x (1/3) = 7.

Division of a Whole number by a Fraction.

DIVISION OF A WHOLE NUMBER BY A FRACTION:

Steps to find Division of whole number by a fraction:

i) Find out the reciprocal of the fraction.

ii) Multiply the whole number with reciprocal of the fraction.

iii) Simplify into its lowest terms.

Required Answer = Whole number x Reciprocal of the Fraction.

 

Solve the following:

1) 8 ÷  1/5

Solution:

Given: Whole number = 8; Fraction = 1/5.  

i) Reciprocal of the fraction = 5.

ii) Multiplying whole number with reciprocal of the fraction.

  8 x 5 = 40 , required answer.        

 

2) 5 ÷   1/6

Solution:

Given: Whole number = 5 ; Fraction = 1/6.

Reciprocal of the fraction = 6.

Required Answer = Whole number x Reciprocal of the fraction.

                                =  5 x 6 = 30.

 

3) 9 ÷  2/3

Solution:

Given: Whole number = 9 ; Fraction = 2/3.

Reciprocal of the fraction = 3/2.

Required answer = Whole number x Reciprocal of the fraction.

                             = 9 x  (3/2) = 27/2.

 

4) 4 ÷ 2/3

Solution:

Given: Whole number = 4 ; Fraction = 2/3.

Reciprocal of the fraction = 3/2.

Required answer = Whole number x Reciprocal of the fraction.

                             = 4 x (3/2) = 6.

Division of Fraction by a Fraction.

DIVISION OF FRACTION BY A FRACTION:

Steps to find the result when a fraction is divided by another fraction:

i) Write the divisor in terms of its reciprocal.

ii) Multiply the dividend with reciprocal of the divisor.

iii) Simplify into its lowest terms.

Required Answer = Dividend x Reciprocal of the Divisor.

 

Solve the following:

1)  15/6  ÷  3/4

Solution:

Given: Dividend = 15/6 ; Divisor = 3/4

i) Reciprocal of the Divisor = 4/3.

ii)   Required Answer =  Dividend x  Reciprocal of the divisor

                                       =  (15/6)   x  (4/3)

iii) Simplifying into its lowest terms:

=  (15x4) / (6x3) = (5x2) / 3 = 10/3.

 

2)  21/28  ÷  3/7

Solution:

Given: Dividend = 21/28 ; Divisor = 3/7

Reciprocal of divisor = 7/3.

Required Answer = Dividend x Reciprocal of the Divisor 

=  (21/28) x (7/3) = (21x7) / (28x3)

 = 7/4.   ( simplify into Lowest terms :  3x7  /  4x3 =  7/4 )

 

3)  2 4/5  ÷  7/2

Solution:

Given: Dividend =  2 4/5 ; Divisor = 7/2

Converting Dividend: mixed fraction into fraction

2 4/5 = 14/5.

Reciprocal of the Divisor = 2/7.

Required Answer  =  Dividend x  Reciprocal of the divisor 

                                = 14/5  x  2/7  =  (14x2) / (5x7) =  4/5.

 

4) 8/9 ÷  5 1/3

Solution:

Given: Dividend = 8/9 ; Divisor = 5 1/3

Converting Divisor(mixed fraction)  into Fraction:

 5 1/3 = 16/3.

Reciprocal of the Divisor = 3/16.

Required Answer = Dividend x  Reciprocal of the divisor 

                               =  (8/9)  x  (3/16)  =  (8x3) / (9x16)  

                               =  1/6.

Multiplication of a Whole number by a Fractional number.

MULTIPLICATION OF A WHOLE NUMBER BY A FRACTIONAL NUMBER:

Steps to multiply a whole number by a fractional number:

i) Write the whole number as a fractional number.

ii) Multiply the numerators of the fractions.

iii) Multiply the denominators of the fractions.

iv) Simplify into lowest terms.

 

Find the Product:

1) 10 x  3/5

Solution:

Given: whole number = 10 ; fraction = 3/5.

Required product = 10/1 x 3/5 = (10x3) / 5 = 30/5 = 6.

2) 16 x  5/4

Solution:

Given: Whole number = 16 ;  fraction = 5/4.

Required Product = 16/1  x  5/4 =  ( 16x5 ) / 4 = 20.

 

3) 6 2/7  of 7.

Solution:

Given: Whole number = 7; mixed fraction = 6 2/7.

Converting mixed fraction into fraction:

((Whole number x denominator) + numerator ) / denominator.

Whole number = 6 ; numerator = 2 ; denominator = 7.

 6 2/7 = 44/7.

Required Product = 7 of  44/7 =  7 x  44/7  

                              = ( 7/1  x  44/7 ) = 44.

 

4) 1 1/15  of  15

Solution:

Given: Whole number = 15 ; Mixed fraction = 1 1/15

Converting mixed fraction into fraction:

1 1/15 = 16/15.

Required Product = 15  of  16/15  =  15 x  16/15

                              = ( 15/1  x  16/15 ) =  16.

 

5)  5 1/5 of 10.

Solution:

Given: Whole number = 10; Mixed fraction = 5 1/5.

Converting mixed fraction into fraction:

5 1/5 = 26/5.

Required Product = 10 of  26/5 = 10  x  26/5

                              = ( 10/1  x  26/5 ) = 2 x 26 = 52. 

   

Multiplication of Fractions.

MULTIPLICATION OF FRACTIONAL NUMBERS:

Steps to Multiply Fractions:

i) Multiply the numerators of the given fractions, which is the new numerator.

ii) Multiply the denominators of the given fractions, which is the new denominators.

iii) Simplify the obtained new numerators and denominators into its Lowest terms, if required (cancel out the common factors wherever possible) .

 

Solve the Following:

1)  5/8  x  8/15

Solution:

Given: Numerators = 5, 8 ; Denominators = 8, 15.

New numerator =  5 x 8 = 40.

New Denominator = 8 x 15 = 90.

Thus, required Product is = 40/90 = 4/9.

 

2)  26/33 x 22/39

Solution:

Given: Numerators = 26 , 22 ; Denominators = 33, 39.

Required Product =  (26x22) / (33x39) ; reducing into lowest terms.

                           = 4/9;  (26/39 = 2/3 ; 22/33 = 2/3; Thus: (2/3) x (2/3) = 4/9).

 

3)  (2/11) x  (3 /4).

Solution:

Given : Numerators = 2, 3 ; Denominators = 11, 4

 Required Product = (2x3) / (11x4) ; reducing into Lowest terms

                               =  (1x3) / (11x2)  ( Since : 2/4 = 1 /2)

                              = 3 / 22.

 

4)  1/5  x  3/ 4

Solution:

Given: Numerator = 1, 3 ; Denominator = 5, 4.

Required Product =  (1x3) / (5x4)

                                = 3 / 20.

 

5)  7/7 x  2/6

Solution:

Given: Numerator = 7, 2 ; Denominator = 7, 6.

Required Product = (7x2) / (7x6); reducing into lowest terms.

                               = 1/3.  (7/7 = 1; 2/6 = 1/3; Thus: 1 x 1/3 =1/3).