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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!

By
Jason Marshall, PhD
April 26, 2013
Episode #151

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What Are Algebraic Expressions?

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.

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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.

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