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bradles0 t1_iybr5rp wrote

remember what 1+2x3 actually MEANS - multiplication is a shorthand for multiple additions, and further up pemdas exponents are multiple multiplications; so you simplify back down the line.

1+2x3^3=1+2x(3x3x3)=1+((3+3+3)+(3+3+3)+(3+3+3))+((3+3+3)+(3+3+3)+(3+3+3))=55

The other reason is the practical considerations - if you have 5 boxes of a dozen eggs and 2 extra eggs, you have 5x12+2 eggs; the standard case for multiplication will be rows + columns + leftovers, and there are FAR fewer cases where you care adding more rows or columns instead of adding in the leftovers, so it's easier to note the special times when you are adding more columns than the times when you are adding the leftovers.

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