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Friday, February 10, 2012

Translating English phrases into Algebraic Expressions

As always, it's a good idea to have pencil and paper handy.  After you understand the concept being taught, pause the video to see if you're able to work the problems before the answers are shown.

A variable is a letter that is used to express an unknown number.

"Less Than" and "Subtracted From"
The phrases "less than" or "subtracted from" indicate that the first variable or number mentioned is being taken from the second number or variable mentioned.
So when you see these phrases, you will know that the expression will be written in the opposite order as they are mentioned in the sentence.

►If you have $85.00 and I have $10.00 less than you, I have $75.00.
If I were to express this in an English phrase (or word phrase), I might say,
10 less than y
But I would not write 10 - y; instead I would write y - 10.

►Suppose I say, "$267 was subtracted from my bank account!"
I will use b for the bank account, and write b - 267 

(1)  Intro to algebraic expressions

When you see the phrases product of, sum of, quotient of, or difference of, there will be at least 2 terms to be calculated.
The product of 6 and a number
The sum of 3 and 9
The quotient of 28 and a number
The difference of 23 and 16

(2) Professor Perez and Charlie introduce this ↑ concept, then show how you can apply this knowledge to longer algebraic expressions.
At 4:35, he shows how to go from algebraic expressions back to English phrases.  This really helps in understanding the key phrases.  Very good!

(3) More Practice.
►At 0:50 there is a chart with phrases that can be used to indicate the 4 operations of multiplication, division, addition, and subtraction.  (such as more than, in addition to, greater, etc.)
It might be useful to pause the video and write these down to keep on hand.

►At 1:10, instruction begins.
He refers to "less than" and "subtracted from" as switch phrases.
He goes rather quickly,  but you should be able to understand these problems if you watched the first two videos.
Pause the video if you need to think it through.  Write down any examples you find helpful.

"John has twice as many quarters as dimes."  Should this be 2q = d or q = 2d?

(4) Even More Practice
Again, at the beginning of this video, there is a chart with phrases used to indicate the 4 operations.  Check to see if there are any additional phrases to the ones in the previous video.
►Pause at 1:20 to see some words and phrases used in place of the = sign.
►At 4:00, there are a few word problems.

"Algebraic Expressions" vs. "Algebraic Equations."
• An expression is like a phrase - incomplete.  There is no = sign, no answer.
• An equation has the = sign.

►The equals sign is like a verb: "is"     5x = 10.  5x is 10.
Words without a verb can be phrases, or in algebra, expressions.
An algebraic expression has no verb.  No "is."

These videos in this blog post are teaching how to write algebraic expressions.
That probably means you'll be learning equations next.  Yay!  

I L♥ve algebra!  =)

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