We explore the relationship between young, embedded binaries and their parent cores, using observations within the Perseus Molecular Cloud. We combine recently published VLA observations of young stars with core properties obtained from SCUBA-2 observations at 850 um. Most embedded binary systems are found toward the centres of their parent cores, although several systems have components closer to the core edge. Wide binaries, defined as those systems with physical separations greater than 500 au, show a tendency to be aligned with the long axes of their parent cores, whereas tight binaries show no preferred orientation. We test a number of simple, evolutionary models to account for the observed populations of Class 0 and I sources, both single and binary. In the model that best explains the observations, all stars form initially as wide binaries. These binaries either break up into separate stars or else shrink into tighter orbits. Under the assumption that both stars remain embedded following binary breakup, we find a total star formation rate of 168 Myr^-1. Alternatively, one star may be ejected from the dense core due to binary breakup. This latter assumption results in a star formation rate of 247 Myr^-1. Both production rates are in satisfactory agreement with current estimates from other studies of Perseus. Future observations should be able to distinguish between these two possibilities. If our model continues to provide a good fit to other star-forming regions, then the mass fraction of dense cores that becomes stars is double what is currently believed.
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