Why? With the coefficients, our reactants would be: 12 carbons, 22 hydrogens, and 35 oxygens.
To obey the law of conservation of mass, we would have to have an equal amount of each of those elements on the products side, since so much of that element needs to form an equal amount on the other side.
So, with those coefficiens, our products would be: 12 carbons total, 35 oxygens total, and 22 hydrogens total. If we compare to the reactants side, they are all equal!
And, since 1 or 11 cannot be simplifyed any smaller, we know the equation is completely balanced.
