What Are Algebraic Expressions?
How can you spot an algebraic expression in the wild? And how can you navigate the stormy seas of translating English phrases into algebraic expressions? Math Dude has the answers!
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The Ambiguity of Language
So, did you run into any problems? You should have! In case you haven’t figured it out, the problem is that the last two English phrases can be interpreted in multiple ways. For example, the second problem, “two plus eight times six,” could be translated as
( 2 + 8 ) x 6
But it could also be translated as
2 + ( 8 x 6 )
Do you see why either of these could be correct translations? This example makes it clear that math is a much better way to express this sort of thing than English. After all, math is designed to be unambiguous…normal spoken language is definitely not!
How to Deal with Ambiguity in Expressions
But not to worry because the good folks who came before us have come up with a way to deal with this problem. Actually, they’ve come up with two. The first is really just a guideline to help you avoid getting bitten: It says that whenever you’re communicating mathematical ideas using English, you need to be careful…extremely careful. I was intentionally sloppy with the way I stated the problems earlier, and you can see the consequences. But you can avoid the majority of these problems simply by clearly communicating what you’re saying and by anticipating any ambiguities.