It has been proven that a quantum computer is superior to an electronic computer in solving some NP problems. Based on quantum operations, this article proposes a new quantum sum and quantum multiplication, and then a floating-point quantum multiplier and a fixed-point quantum divisor are created based on fixed-point number operations. These studies lay the foundation for the quantum implementation of digital filters. This article presents a new method for calculating the sumator on a quantum computer. This method uses the quantum Fourier Transform (QFT) and reduces the number of qubits needed for the connection, eliminating the need for temporary bit transfer. This approach also allows adding a classical number to a quantum superposition without encoding the classical number in a quantum register. This method also allows for massive parallelization during its execution. The QFT-based addition and multiplication capabilities are improved with some changes. The proposed operations are compared with the operations of approximate quantum arithmetic.