Large Language Models (LLMs) have shown remarkable performance across various tasks, yet significant disparities remain for non-English languages, and especially native African languages. This paper addresses these disparities by creating approximately 1 million human-translated words of new benchmark data in 8 low-resource African languages, covering a population of over 160 million speakers of: Amharic, Bambara, Igbo, Sepedi (Northern Sotho), Shona, Sesotho (Southern Sotho), Setswana, and Tsonga. Our benchmarks are translations of Winogrande and three sections of MMLU: college medicine, clinical knowledge, and virology. Using the translated benchmarks, we report previously unknown performance gaps between state-of-the-art (SOTA) LLMs in English and African languages. Finally, using results from over 400 fine-tuned models, we explore several methods to reduce the LLM performance gap, including high-quality dataset fine-tuning (using an LLM-as-an-Annotator), cross-lingual transfer, and cultural appropriateness adjustments. Key findings include average mono-lingual improvements of 5.6% with fine-tuning (with 5.4% average mono-lingual improvements when using high-quality data over low-quality data), 2.9% average gains from cross-lingual transfer, and a 3.0% out-of-the-box performance boost on culturally appropriate questions. The publicly available benchmarks, translations, and code from this study support further research and development aimed at creating more inclusive and effective language technologies.