Atoms are related to balancing equations because the amount of atoms on the left of the equation (reactants) needs to be the same amount on the right (products).
For example, 2H₂ + O₂ → 2H₂O
If you count the amount of hydrogen atoms on both sides each, there would be 4 (make sure to multiply the coefficient by the subscripts).
If you count the amount of oxygen atoms on both sides each, there will be 2 of them (2 in a molecule of oxygen)
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