FOLD-R++ is a highly efficient and explainable rule-based machine learning algorithm for binary classification tasks. It generates a stratified normal logic program as an (explainable) trained model. We present an improvement over the FOLD-R++ algorithm, termed FOLD-SE, that provides scalable explainability (SE) while inheriting all the merits of FOLD-R++. Scalable explainability means that regardless of the size of the dataset, the number of learned rules and learned literals stay small and, hence, understandable by human beings, while maintaining good performance in classification. FOLD-SE is competitive in performance with state-of-the-art algorithms such as XGBoost and Multi-Layer Perceptrons (MLP). However, unlike XGBoost and MLP, the FOLD-SE algorithm generates a model with scalable explainability. The FOLD-SE algorithm outperforms FOLD-R++ and RIPPER algorithms in efficiency, performance, and explainability, especially for large datasets. The FOLD-RM algorithm is an extension of FOLD-R++ for multi-class classification tasks. An improved FOLD-RM algorithm built upon FOLD-SE is also presented.