Is 3 5 - 7 8 = 7 8 - 3 5 ?

Given 3 5 - 7 8 = 7 8 - 3 5 LHS: 3 5 - 7 8 = 24 - 35 40 ∵ L.C.M. of 5 and 8 is 40 = - 11 40 RHS: 7 8 - 3 5 = 35 - 24 40 ∵ L.C.M. of 5 and 8 is 40 = 11 40 Therefore, LHS≠RHS Hence, 3 5 - 7 8 ≠ 7 8 - 3 5 . We conclude that subtraction is not commutative for rational numbers.

Is 3 5 ÷ 7 8 = 7 8 ÷ 3 5 ? So, what do you conclude?

Given, 3 5 ÷ 7 8 = 7 8 ÷ 3 5 LHS = 3 5 ÷ 7 8 = 3 5 × 8 7 = 24 35 RHS = 7 8 ÷ 3 5 = 7 8 × 5 3 = 35 24 Therefore, LHS ≠ RHS. Hence, 3 5 ÷ 7 8 ≠ 7 8 ÷ 3 5 We conclude that division is not commutative for rational numbers.

Verify the distributive property a × ( b + c ) = ( a × b ) + ( a × c ) for the rational numbers a = - 1 2 , b = 2 3 and c = - 5 6 .

We need to check a = - 1 2 , b = 2 3 and c = - 5 6 satisfies a × b + c = a × b + a × c . Now, a × ( b + c ) = - 1 2 × 2 3 + - 5 6 = - 1 2 × 2 × 2 + - 5 × 1 6 = - 1 2 × 4 + - 5 6 = - 1 2 × - 1 6 ⇒ a × b + c = 1 12 And a × b + a × c = - 1 2 × 2 3 + - 1 2 × - 5 6 = - 2 6 + 5 12 = ( - 2 × 2 ) + 5 × 1 12 = - 4 + 5 12 = 1 12 ⇒ a × b + a × c = 1 12 Therefore, a × ( b + c ) = ( a × b ) + ( a × c ) Hence, multiplication is distributive over addition for rational numbers.