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My kid, 5 years old, knows addition, subtraction and multiplication now, of course, in a basic level.

Also he understands that parentheses means "whichever inside shall be computed first".

When I try explain the rules of "taking off the parentheses", he seems thinks "so long as we can compute, why take it off?"

For example, $10 - (5-3) = 10 - 2 = 8$, why shall it be done as $10 - (5-3) = 10 -5 +3 = 5 + 3 = 8$?

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    $\begingroup$ One possible place where this could be explained is when 'multiplying by making fives/tens' or other similar calculations where one way is easy to remember and another less so: 3(5+1) = 15 + 3 = 18 vs. 3(6) = 18 (memorized) 3(10+3) = 3(10)+3(3) = 30+9 = 39 vs. 3(13)=39 (memorized) Understanding this leads to the standard base-10 algorithm for multiplication. Any time a student asks for why they should learn something that they can do the 'easy way,' give them a scenario when the new way IS the 'easy way'. $\endgroup$ – Opal E Feb 26 at 2:24
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    $\begingroup$ @TommiBrander 5 years old. Title updated. $\endgroup$ – athos Feb 26 at 6:51
  • $\begingroup$ "why take it off?" - because one can. Sometimes it makes sense, sometimes not. Without variables, it is never necessary. $\endgroup$ – Jasper Feb 28 at 6:52
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Why take off the parentheses?

Because sometimes "taking off the parentheses" results in an easier to calculate expression. For example,

$$123456789-(-9876543210+123456789)$$ is easier to evaluate by using $123456789+9876543210-123456789=9876543210$.

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