Question

Write & verify the Commutative property by taking two rational numbers.

Answer 1

commutative property under ,addition subtraction, multiplication ,division

Answer 2

Answer:

Property of Commutative law by taking two rational numbers.

Let  $\frac { a }{ b }$ and $\frac { c }{ d }$ are two rational numbers.

$\frac { a }{ b } +\frac { c }{ d } \quad =\quad \frac { c }{ d } +\frac { a }{ b }(Addition)$

$\frac { a }{ b } \times \frac { c }{ d } \quad =\quad \frac { c }{ d } \times \frac { a }{ b }(Multiplication)$

Let two rational numbers are  $\frac { 1 }{ 5 }$ and $\frac { 1 }{ 7 }$.

Commutative property by taking two rational numbers(Addition)

$\frac { 1 }{ 5 } +\frac { 1 }{ 7 } \quad =\quad \frac { (7+5) }{ 35 } \quad =\quad \frac { 12 }{ 35 } \frac { 1 }{ 7 } +\frac { 1 }{ 5 } \quad =\quad \frac { (7+5) }{ 35 } \quad =\quad \frac { 12 }{ 35 }$

∴ $\frac { 1 }{ 7 } +\frac { 1 }{ 5 } \quad =\quad \frac { 1 }{ 7 } +\frac { 1 }{ 5 } \quad =\quad \frac { 12 }{ 35 }$ Proved

Commutative property by taking two rational numbers (Multiplication)

$\frac { 1 }{ 5 } \times \frac { 1 }{ 7 } \quad =\quad \frac { 1 }{ 35 } And \frac { 1 }{ 7 } +\frac { 1 }{ 5 } \quad =\quad \frac { 1 }{ 35 }$

∴ $\frac { 1 }{ 5 } \times \frac { 1 }{ 7 } \quad =\quad \frac { 1 }{ 7 } +\frac { 1 }{ 5 } \quad =\quad \frac { 1 }{ 35 }$ Proved.