Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions intended to improve understanding of both individual fractions and fraction addition. The framework, Putting Fractions Together (PFT), emphasizes that both individual fractions and sums of fractions are composed of unit fractions and can be represented by concatenating them (putting them together). To illustrate, both "3/9" and "2/9 + 1/9" can be represented by concatenating three 1/9s; similarly, 2/9 + 1/8 can be represented by concatenating two 1/9s and one 1/8. Interventions based on the PFT framework were tested in 2 experiments with fourth, fifth, and sixth grade children. The interventions led to improved performance on number line estimation and magnitude comparison tasks involving individual fractions and sums of fractions with equal and unequal denominators. Especially large improvements were observed on relatively difficult unequal-denominator fraction sum problems. The findings suggest that viewing individual nonunit fractions and sums of fractions as concatenations of unit fractions provides a sound conceptual foundation for improving children's knowledge of both. We discuss implications of the research for teaching and learning fractions, children's numerical development, and mathematics education in general. [The article was published in "Journal of Educational Psychology" (EJ1291033).]