This paper investigates children's understanding of the inverse relationship between addition and subtraction, a fundamental logical principle in arithmetic. The study examines whether preschool children can apply this understanding to approximate number problems, both in symbolic and non-symbolic forms. In three experiments, 5- to 6-year-old children were presented with problems involving successive addition and subtraction, either in non-symbolic (dot arrays) or symbolic (number words and Arabic numerals) form. The results show that children performed significantly better on problems involving an inverse transformation (e.g., $x + y - y$) compared to control problems (e.g., $x + y - z$), indicating their ability to recognize and use the inverse relationship. However, they did not perform better on exact arithmetic problems involving symbolic representations of large numbers, suggesting that their understanding of inversion is limited to approximate number representations. These findings suggest that children's mastery of arithmetic principles may first be expressed in contexts involving approximate number representations and only later extend to exact arithmetic tasks. The implications for arithmetic instruction are discussed, highlighting the potential benefits of incorporating approximate symbolic and non-symbolic arithmetic problems to help children understand the underlying logical principles of arithmetic.This paper investigates children's understanding of the inverse relationship between addition and subtraction, a fundamental logical principle in arithmetic. The study examines whether preschool children can apply this understanding to approximate number problems, both in symbolic and non-symbolic forms. In three experiments, 5- to 6-year-old children were presented with problems involving successive addition and subtraction, either in non-symbolic (dot arrays) or symbolic (number words and Arabic numerals) form. The results show that children performed significantly better on problems involving an inverse transformation (e.g., $x + y - y$) compared to control problems (e.g., $x + y - z$), indicating their ability to recognize and use the inverse relationship. However, they did not perform better on exact arithmetic problems involving symbolic representations of large numbers, suggesting that their understanding of inversion is limited to approximate number representations. These findings suggest that children's mastery of arithmetic principles may first be expressed in contexts involving approximate number representations and only later extend to exact arithmetic tasks. The implications for arithmetic instruction are discussed, highlighting the potential benefits of incorporating approximate symbolic and non-symbolic arithmetic problems to help children understand the underlying logical principles of arithmetic.