  This paper presents a novel approach to automatically solving arithmetic word
problems. This is the first algorithmic approach that can handle arithmetic
problems with multiple steps and operations, without depending on additional
annotations or predefined templates. We develop a theory for expression trees
that can be used to represent and evaluate the target arithmetic expressions;
we use it to uniquely decompose the target arithmetic problem to multiple
classification problems; we then compose an expression tree, combining these
with world knowledge through a constrained inference framework. Our classifiers
gain from the use of {\em quantity schemas} that supports better extraction of
features. Experimental results show that our method outperforms existing
systems, achieving state of the art performance on benchmark datasets of
arithmetic word problems.
