# What is the property of addition called when you break 97 into 100 - 3?

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.

## 2 Answers

\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}

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

• 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. – CJ Dennis Feb 8 '16 at 0:10
• 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. – Carl Christian Feb 8 '16 at 10:36