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The rules of arithmetic follow the famous rule of "Please, My Dear Aunt Sally": that is, you do operations in Parentheses, then Multiplication, then Division, then Addition, then Subtraction in that order, working from left to right.
This problem has no parentheses, so it can be written as
9 * 9 + 9 / 9 + 9 + 9
If you do the multiplication and division first, you get
9 * 9 + 9 / 9 + 9 + 9 =
81 + 1 + 9 + 9
which can now be done left to right for an answer of 100.


-- More --
To show how parentheses can change the order AND the answer, here are two possible rearrangements:


First: 9 * (9 + 9/9) + 9 + 9. You perform the operations inside the parentheses FIRST, still using MDAS:
9 * (9 + 9/9) + 9 + 9 = 9 * (9 + 1) + 9 + 9 = 9 * 10 + 9 + 9 = 90 + 9 + 9 = 108


Second: 9 * (9 + 9) / 9 + 9 + 9 = 9 * 18 / 9 + 9 + 9 = 162 / 9 + 9 + 9 = 18 + 9 + 9 = 36
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Q: In third grade How can you work out 9 times 9 plus 9 divided by 9 plus 9 plus 9?
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