This study explores preschool children's understanding of the inverse relationship between addition and subtraction. The research indicates that preschool children can recognize and apply this logical principle in non-symbolic, approximate arithmetic problems, but not in exact symbolic problems. The study involved three experiments with preschool children, testing their ability to solve problems involving addition and subtraction of large approximate numbers. In Experiment 1, children were presented with non-symbolic, large approximate arithmetic problems. They were more accurate on inverse problems (e.g., x + y - y) than on control problems (e.g., x + y - z), suggesting they understood the inverse relationship. However, their performance was not explained by simple comparisons of set sizes or continuous variables. In Experiment 2, children were presented with symbolic representations of numbers. They performed better on inverse problems than on control problems, indicating they could identify and use the inverse relationship. However, they did not perform above chance on control problems, suggesting their success was not due to a general strategy. In Experiment 3, children were presented with exact comparisons. They performed at chance levels on inverse problems, indicating they did not recognize the inverse relationship when exact comparisons were required. The findings suggest that preschool children have a general understanding of the inverse relationship between addition and subtraction, particularly when dealing with approximate, non-symbolic numbers. This understanding may be based on an abstract, conceptual grasp of numerical relationships rather than formal instruction. The study highlights the importance of incorporating approximate arithmetic problems in early mathematics education to build on children's innate understanding of numerical relationships.This study explores preschool children's understanding of the inverse relationship between addition and subtraction. The research indicates that preschool children can recognize and apply this logical principle in non-symbolic, approximate arithmetic problems, but not in exact symbolic problems. The study involved three experiments with preschool children, testing their ability to solve problems involving addition and subtraction of large approximate numbers. In Experiment 1, children were presented with non-symbolic, large approximate arithmetic problems. They were more accurate on inverse problems (e.g., x + y - y) than on control problems (e.g., x + y - z), suggesting they understood the inverse relationship. However, their performance was not explained by simple comparisons of set sizes or continuous variables. In Experiment 2, children were presented with symbolic representations of numbers. They performed better on inverse problems than on control problems, indicating they could identify and use the inverse relationship. However, they did not perform above chance on control problems, suggesting their success was not due to a general strategy. In Experiment 3, children were presented with exact comparisons. They performed at chance levels on inverse problems, indicating they did not recognize the inverse relationship when exact comparisons were required. The findings suggest that preschool children have a general understanding of the inverse relationship between addition and subtraction, particularly when dealing with approximate, non-symbolic numbers. This understanding may be based on an abstract, conceptual grasp of numerical relationships rather than formal instruction. The study highlights the importance of incorporating approximate arithmetic problems in early mathematics education to build on children's innate understanding of numerical relationships.