If the product of two rational numbers is (-9)/16 and one of them is (-4)/15, find the other number.

Let the required rational number be x.

∴ x × (-4/15) = -9/16

⇒ x = (-9/16) ÷ (-4/15) = (-9/16) × (15 / -4)

[Reciprocal of (-4/15) = (15 / -4)]

= (-9 × 15) / (-16 × 4) = 135/64 = 2⁷/₆₄

Hence, the required rational number = 2⁷/₆₄.