We introduce approximations to arithmetical data types called arithmetics by proxy or proxy arithmetics. Focusing on the common meadow of rational numbers, we examine the effect of imposing bounds on the numbers and finiteness on algebras that approximate the rationals. Starting with an established set of equations for common meadows, we explore sets of equational axioms for these approximating algebras. Then we give a new general algebraic construction that may serve as a way of making proxies for arbitrary data types. We apply the construction to the arithmetical case. Finally, we return to the sets of equations using notions of equality that are different from standard first order equality.