Verify - 10 17 × 2 5 = 2 5 × - 10 17

We know that the product of two rational numbers = Product of Numerators Product of Denominators . We leave the product in its lowest form with a positive denominator. Thus, we have, LHS = - 10 17 × 2 5 = - 10 × 2 17 × 5 = - 2 × 5 × 2 17 × 5 = - 4 17 . Again, RHS = 2 5 × - 10 17 = 2 × - 10 5 × 17 = 2 × ( - 2 ) × 5 5 × 17 = - 4 17 . Thus, we have, LHS = RHS or - 10 17 × 2 5 = 2 5 × - 10 17 . Hence, proved.

Verify - 11 15 × 4 19 = 4 19 × - 11 15

We know that the product of two rational numbers = Product of Numerators Product of Denominators . We leave the product in its lowest form with a positive denominator. Thus, we have, LHS = - 11 15 × 4 19 = - 11 × 4 15 × 19 = - 44 285 . Again, RHS = 4 19 × - 11 15 = 4 × - 11 19 × 15 = - 44 285 . Thus, we have, LHS = RHS or - 11 15 × 4 19 = 4 19 × - 11 15 . Hence, proved.

Verify 7 16 × - 24 49 × 28 15 = 28 15 × 7 16 × - 24 49

We know that the product of rational numbers = Product of Numerators Product of Denominators . We leave the product in its lowest form with a positive denominator. Thus, we have, LHS = 7 16 × - 24 49 × 28 15 = 7 × - 24 × 28 16 × 49 × 15 = 7 × ( - 1 ) × 2 × 3 × 4 × 4 × 7 4 × 4 × 7 × 7 × 3 × 5 = - 2 5 . Again, RHS = 28 15 × 7 16 × - 24 49 = 28 × 7 × - 24 15 × 16 × 49 = 4 × 7 × 7 × ( - 1 ) × 2 × 3 × 4 3 × 5 × 4 × 4 × 7 × 7 = - 2 5 . Thus, we have, LHS = RHS or 7 16 × - 24 49 × 28 15 = 28 15 × 7 16 × - 24 49 . Hence, proved.