It's actually quite simple, once you get the idea.
To lose fat, you must take in fewer calories than what it takes to maintain your current bodyweight.
Here is an example of the math:
Through diet and exercise together you have created a caloric deficit of 1000 calories.
One pound of fat contains 3500 calories, therefore if you have a caloric deficit of 1000 calories a day for seven days you will burn 7000 calories and, theoretically, lose 2 pounds of fat.
A good rule of thumb to start with is to eat ten times your bodyweight in calories (e.g. if you weigh 150 pounds, eat 1500 calories).
In the real world, these numbers are simply estimates. There is no way to control everything you eat or your metabolic rate or exactly how many calories you burn during exercise. Follow the principles and don't concern yourself too much with the numbers.
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