Operads are a tool blending algebra and geometry together: they describe intricate algebraic structures, in which elements can be multiplied in many different ways and deformed into each other. They admit applications in many different parts of mathematics, such as differential topology, number theory, and mathematical physics. In this research we investigate operads by finding ways of breaking them up into simpler pieces and then reconstructing them. We will in particular apply our results to the study of embedding spaces between manifolds.