The simple rule to follow is that whatever is done on the Left Hand Side of the equation must be repeated on the Right Hand Side of the equation to keep it in 'balance'
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You use order of operations in equations that have more than one type of operation going on (for example, an equation with parenthesis, addition, and multiplication). You would use order of operations in equations like that so you know which operation to do first.
No professions use order of operations. It is just a method of solving an equation.
Why? - Mainly to help in solving equations.
if you are good at math, you would know. I'm not being mean, but sometimes it takes a little help from an adult.
It is essential to use balanced equations when solving stoichiometric problems because each kind of atom has to be the same on both sides of the equation. The chemical reactions that take place are molar ratios.