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Sometimes it's easier to add numbers when you recognise that they're close to some round number, and then add the differences separately.

$$97+198$$

$$=(100-3)+(200-2)$$

$$=(100+200)+(-3-2)$$

$$=300-5$$

$$=295$$

What is this property of addition called? I have found "commutative" but I'm not sure that this is the right word.

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2 Answers 2

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\begin{align} 97+198&=\\(100-3)+(200-2)&=\\ 100+(-3+200)-2&=\quad\quad&\text{Associativity.}\\ 100+(200-3)-2&=\quad\quad&\text{Commutativity.}\\ (100+200)-3-2&=\quad\quad\quad\quad\quad&\text{Associativity.}\\ \vdots \end{align}

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You are exploiting both the commutitative law $a + b = b + a$ and the associative law $a + (b + c) = (a + b) + c$

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  • $\begingroup$ This answer is more descriptive and arguably better, but the answer provided by @YoTengoUnLCD is clearer because it is visual. It could do with a short descriptive paragraph like this answer has. $\endgroup$
    – CJ Dennis
    Feb 8, 2016 at 0:10
  • $\begingroup$ I am happy that you received answers that were useful to you. When face to face with a student I find it relatively easy to pick the appropriate answers, because I get to see the physical reaction to my words, i.e. changes in body language. This is of course impossible in this forum. $\endgroup$ Feb 8, 2016 at 10:36

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