The reorder of operations

The community of maths users the world over agrees that when evaluating an expression or calculation, some operations should be done before others. Mostly it's to prevent us having to be needlessly specific about what order to do calculations in, mathematicians being very concerned with efficient communication.

My problem with the order of operations as usually stated is this: it's wrong! It's wrong because you almost always don't do the operations in the order described. You don't do all the multiplications before all the additions, and instead will often quite a few of the additions first because they are easier. And you don't do the multiplications in the order they come, but rearrange them into some other easier order. And you often don't do the brackets first, but instead choose expand them out in order to make the calculation easier.

You can read the rest of this blog post, and the other posts in the series across the years, in PDF form here.

The titles of the five blog posts are:

• The reorder of operations
• (Holding it together)
• The Operation Tower
• Replacing
• Sticky operations