Definitely cardio should be done before eating.
The human body (unless conditioned otherwise by something like the Adkins diet) will burn carbohydrates during physical activity before burning fat. It's part of how carbohydrates are turned into energy in the body vs how fat is turned into energy in the body, and the amount of calories (bodily action fuel) created by this process.
That being said, if the body contains fewer carbohydrates before beginning a workout, then the body will have fewer carbohydrates to burn for energy before needing to burn fat for energy. However the very nature of the calories created by the processing of these different materials create a different kind of energy.
There is a significantly larger amount of energy created by the processing of carbohydrates vs fats. Which means the workout feels more tiring than it would feel had the individual engaging in it had eaten before working out.
More importantly than whether to engage in cardio before or after (which I think the majority consensus would be before) its what kind of cardio. While distance running requires a lot from the lungs, it doesn't burn very much energy/sec.
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