With the emergence of chain-of-thought (CoT) reasoning, large language models (LLMs) have demonstrated substantial potential in tackling multi-step reasoning tasks. However, existing CoT-based approaches primarily emphasize either semantic understanding or the enhancement of the reasoning process, with limited efforts to address both aspects concurrently. As a result, these methods struggle with suboptimal performances due to semantic misunderstanding, calculation errors, or step-missing errors when solving complex mathematical problems. In this paper, we propose a novel Deep Understanding and Extended Reasoning (DUER) prompting method for solving mathematical problems, which seamlessly integrates semantic comprehension with reasoning enhancement. Specifically, DUER samples the most complex examples from the training set, and utilizes a deep understanding module to extract the core question and key information from mathematical problems and an extended reasoning module to generate more detailed reasoning steps for these examples. Finally, these enhanced examples containing the core question and information are used to prompt LLMs to infer the answer to the test question. Extensive experiments on 9 reasoning benchmarks show that our method achieves competitive performances on all datasets and establishes new state-of-the-art on GSM8K, SVAMP, AQuQ, and MATH benchmarks. The code is available at: https://github.com/amazingjj/DUER .