Multiplication of a Whole Number by a Fraction

Multiplication of a Whole Number by a Fraction

We will discuss here about the multiplication of a whole number by a fraction.

Now let us learn the multiplication of fractional numbers.

Let us suppose 6 is multiplied by

13

13

13

 

Fractional Multiplication

         represent 1 …………….                       represent 6 …………….    

Fractional Multiplication Image

 

 

13

13

of 6 means 2

or, 13

13

 of 6 = 13

13

 + 13

13

 + 13

13

+ 13

13

+ 13

13

+ 13

13

= 1+1+1+1+1+13

1+1+1+1+1+13

= 63

63

= 2

Fractional Multiplication Picture

 

 

13

13

of 6 = 13

13

× 6 = 2, the shaded portion.


Fraction of a whole number = Numerator of fractionDenominator of fraction

Numerator of fractionDenominator of fraction

Whole number1

Whole number1

Hence we conclude that, to multiply a fractional number by a whole number we multiply the numerator of the fractional number by the whole number and the denominator of the fractional number by 1. The first product thus obtained is the numerator and the second product is the denominator of the required product.

 

Solved examples on multiplication
of a whole number by a fraction:

1. Multiply the
following:

(i) 1721

1721

by 7.

= 1721

1721

× 7

= 17×721×1

17×721×1

= 17×13×1

17×13×1

= 173

173

= 523

23

(ii) 29

29

by 3

= 29

29

× 3

= 2×39×1

2×39×1

= 2×13×1

2×13×1

= 23

23

 

2. Find the
product: 

(i) 23

23

× 5

= 2×53×1

2×53×1

= 103

103

= 313

13

(ii) 129

29

× 5

= (1 + 29

29

) × 5

= 9+29

9+29

× 5

= 119

119

× 5

= 11×59×1

11×59×1

= 559

559

= 619

19

(iii) 356

56

× 4

= 236

236

× 4

= 23×46×1

23×46×1

= 23×23×1

23×23×1

= 463

463

= 1513

13

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