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Properties of Multiplication of Fractional Numbers

The properties of multiplication of fractional numbers are discussed here.

Property I: If two fractional numbers are multiplied in either order, the product remains the same.

or, The product of two fractional numbers does not change even if we change the order of multiplication.

Let us understand this property with the help of some examples.

For Example:

1. 23 × 75

= 2×73×5

= 1415

And now if you interchange the place of the fractional numbers the product does not change.

75 × 23

= 7×25×3

= 1415

We observe that the product in both the cases are same.

So, 23 × 75 = 75 × 23.


2. (423 × 513) × 15 = 423 (513 × 15)

Properties of Multiplication of Fractional Numbers


3. 13 × 59 = 1×53×9 = 527

    59 × 13 = 5×19×3

 = 527


4. 8 × 57 = 8×57 = 407 = 557

57 × 8 = 5×87 = 407 = 557


5. 38 × 123 = 38 × 1×3+23 = 38 × 53 = 1524 = 58

    123 × 38 = 1×3+23 × 38 = 53 × 38 = 1524 = 58


6. 323 × 4211 = 3×3+23 * 4×11+211 = 113 × 4611 = 463 = 1513

    4211 × 323 = 4×11+211 × 3×3+23= 4611 × 113 = 463 = 1513


Property II: The product of three or more fractional numbers does not change even if we change their groups.

Let us understand this with the help of some examples.


1. 13 × (25 × 47) = 13 × (2×45×7) = 13 × 835 = 8105


(13 × 47) × 25 = (1×43×7) × 25 = 421 × 25 = 8105

47 × (13 × 25) = 47 × (1×23×5) = 47 × 215 = 8105


Note: From the above examples we understand that, changing the order of fractional numbers does not change the product.


Property III: If a fractional number is multiplied by one, the product is the fractional number itself.

or, The product of a fractional number and 1 is the fractional number it self. 

Let us consider some examples.

For Example:

1. 79 × 1 

= 79 × 11

= 7×19×1

= 79

2. 58 × 1

= 58 × 11

= 5×1(8×1

= 58



3. 1519 × 1

= 1519 × 11

= 15×1(19×1

= 1519


4. 2737 × 1 = 27×137 = 2737

5. 434 × 1 = 4×4+34 × 1 = 194 × 1 = 19×14194 = 434

So, we observe that a fraction multiplied by 1 is the fraction itself.


Property IV: If a fractional number is multiplied by zero, the product is zero.

or, The product of a fractional number and 0 is always 0.

Let us consider some examples.

For Example:

1. 311 × 0

= 3×011

= 0


2. 715 × 0

= 7×015

= 0


3. 227 × 0 = 0

4. 234 × 0 = 0


Property V: Multiplicative Inverse Property.

When the product of a fractional number and a whole number is 1, each one is a multiplicative inverse of the other.

Let us consider some examples.

1. 19 × 9 = 1×99 = 99 = 1

Here, 19 the multiplicative inverse of 9 and 9 is the multiplicative inverse of 19


2. 118 × 18 = 1×1818 = 1818 = 1

Here, 118 and 18 are the multiplicative inverse of each other.


Property VI: When the product of two fractional numbers is 1, both are the multiplicative inverse of each other.

Let us consider some examples.

1. 47 × 74 = 2626 = 1

Here, 47 and 74 are multiplicative inverse of each other.

2. 434 × 419 = 4×4+34 × 419 = 194419 19×44×19= 7676 = 1

Here, 434 and 419 are multiplicative inverse of each other.

 Multiplication is Repeated Addition.

● Multiplication of Fractional Number by a Whole Number.

● Multiplication of a Fraction by Fraction.

● Properties of Multiplication of Fractional Numbers.

● Multiplicative Inverse.

● Worksheet on Multiplication on Fraction.

● Division of a Fraction by a Whole Number.

● Division of a Fractional Number.

● Division of a Whole Number by a Fraction.

● Properties of Fractional Division.

● Worksheet on Division of Fractions.

● Simplification of Fractions.

● Worksheet on Simplification of Fractions.

● Word Problems on Fraction.

● Worksheet on Word Problems on Fractions.








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