Here are the solutions of questions along with explanation:Sol. 8- Additive inverse of -7/19 is 7/19.Explanation: Additive inverse means the inverse of sign of a given number i.e. - becomes + and + becomes - .Sol. 9- - (-x)= xi) x=3/5LHS= -(-x) = -(-3/5)= + 3/5= 3/5 RHS= 3/5∵LHS= RHS, ∴ -(-x)= xii) x= -7/9LHS= -(-x)= -{-(-7/9)} = -(+7/9)= -7/9RHS= -7/9∵LHS= RHS, ∴ -(-x)= xiii) x=13/-15LHS= -(-x)= -(-13/-15)= -(13/15)= -13/15RHS= -13/15∵LHS= RHS, ∴ -(-x)= xSol. 10- Verification of x+y= y+x i.e. Commutative property over additioni) x= 1/2, y=1/2LHS= x+y= 1/2+ 1/2= (1+1)/2= 2/2= 1RHS= y+x= 1/2+ 1/2= (1+1)/2= 2/2= 1∵LHS= RHS, ∴x+y= y+xii) x= -2/3, y= -5/6LHS= x+y= -2/3 + (-5/6)= (-4-5)/6= -9/6= -3/2RHS= y+x= -5/6 + (-2/3)= (-5-4)/6= -9/6= -3/2∵LHS= RHS, ∴x+y= y+xSol. 11- Simplification i.e. reducing in the lowest FORM:i) [1/2 × 1/4] + [1/2 × 6]= 1/8 + 3= (1+24)/8=25/8 II) [1/5 × 2/15] - [1/5 × 2/5]= 2/75 - 2/25= (2-6)/75= -4/75Sol. 12- Verification of x × (y× z) = (x × y) × z i.e. Associative law over multiplicationa) x= 1, y= -1/2 and z= 1/4LHS= x × (y× z) = 1 × (-1/2 × 1/4)= 1 × -1/8= -1/8RHS= (x × y) × z= (1 × -1/2) × 1/4= -1/2 × 1/4= -1/8∵LHS= RHS, ∴x × (y× z) = (x × y) × z b) x= 2/3, y= -3/7 and z=1/2LHS= x × (y× z)= 2/3 × (-3/7 × 1/2)= 2/3 × -3/14= -1/7RHS= (x × y) × z = (2/3 × -3/7) × 1/2= -2/7 × 1/2= -1/7∵LHS= RHS, ∴x × (y× z) = (x × y) × z Sol. 13- Verification of x × (y+z)= x × y+ y × z i.e Distributive lawa) x= -1/2, y= 3/4 and z=1/4LHS= x × (y+z)= -1/2 × (3/4 + 1/4)= -1/2 × 1= -1/2RHS= x × y+ y × z= -1/2 × 3/4 + -1/2 × 1/4= -3/8 + (-1/8)= -4/8= -1/2∵LHS= RHS, ∴x × (y+z)= x × y+ y × zb) x= -1/5, y= 2/15 and z= -3/10LHS= x × (y+z)= -1/5 × {2/15 + (-3/10)}= -1/5 × (4-9)/30= -1/5× -5/30= -1/5× -1/6= 1/30RHS= x × y+ y × z= -1/5×2/15 + (-1/5× -3/10)= -2/75 + 3/50= (-4+9)/150= 5/150= 1/30∵LHS= RHS, ∴x × (y+z)= x × y+ y × z