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!
What makes an algebraic expression an algebraic expression? How can you spot one in the wild? And how can you learn to successfully navigate the stormy seas of translating back-and-forth between English phrases and algebraic expressions? Stay tuned because those are exactly the questions we’ll be tackling today.
Sponsor: This podcast is brought to you by Betterment.com. Betterment offers users an easy way to invest. No prior investing experience is required. Users choose how to allocate their money between two pre-set baskets—a stock basket and a bond basket. Signing up takes less than 5 minutes, and money can be added or withdrawn at any time without a fee. Users who sign up at betterment mathdude will receive a $25 account bonus as long as their initial deposit is $250 or more.
How to Spot an Expression?
What exactly does an expression in math look like? Well, here’s an example of an extremely simple expression:
1
Is that really it? Yes, that’s really it—just the number 1. Or perhaps the number 2 or any other number. Technically, these are all examples of expressions because, like all expressions, they’re made from a combination of numbers, variables, parentheses, and operators. While the expression “1” is just a number, not all expressions have to be so simple. For example, the expression “5 + 10” uses two numbers and an operator. It’s still pretty simple, but we can make things that are far more complicated. To see what I mean, here’s an expression containing two numbers, two operators, and a variable
101 • ? + 1,001
If we were so inclined we could go on and on like this creating ever more complicated expressions. But I think that’s enough to give you the idea.
Translating English Phrases Into Expressions
Many people have trouble translating ideas spoken in English into expressions written mathematically. Most often this problem rears its ugly head when people get stuck trying to translate so-called “word problems” into mathematical expressions. These types of problems can be tricky, but a bit of practice with english-to-expression translations (which are a key part of solving most word problems) should help you deal with them. With that in mind, let’s go over a few examples. Let’s start with the phrase
“two plus eight”
What’s the equivalent algebraic expression? That one’s easy, right? Okay, how about
“two plus eight times six”
Or perhaps we should throw a variable into the mix:
“two plus eight times six divided by ?”
What are the equivalent expressions for these phrases? I’ll give you a minute to think about it…and to see if you can discover a big roadblock.
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)x6
But it could also be translated as
2+(8×6)
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.
The second fix is to use the order of operations—aka, PEMDAS. As you’ll recall from our earlier discussion of PEMDAS, the order of operations is a standard method for determining which parts of an arithmetic or algebra problem need to be solved first. Once you know the rules of PEMDAS, you’ll be able to translate those English phrases into ambiguity-free expressions that are sure to make everybody’s lives easier!
Wrap Up
Okay, that’s all the math we have time for today. If you want to learn more about algebra, please check out my book The Math Dude’s Quick and Dirty Guide to Algebra.
Remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too. Finally, please send your math questions my way via Facebook, Twitter, or email at mathdude@quickanddirtytips.comcreate new email.
Until next time, this is Jason Marshall with . Thanks for reading, math fans!
You May Also Like…
About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.
