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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

CRISTINEKAY (Customer)

[00:00:00] I have to simplify the following expression and I do not remember where to start..what steps to I take to simplify the expression?

William S (Tutor)

[00:00:12] Hello! I think I can help you with this problem.

CRISTINEKAY (Customer)

[00:00:25] Hello

[00:00:29] thank you'

William S (Tutor)

[00:00:39] When we simplify fractions, it's important to remember that we have to divide each term by the denominator individually.

[00:00:54] In this case, you can think of this fraction like this:

CRISTINEKAY (Customer)

[00:01:20] okay

William S (Tutor)

[00:01:40] For this problem, though, we can take a different solution

[00:02:01] Both 15 and 10 are divisible by 5, so we can factor a 5 out of the numerator - are you familiar with this?

CRISTINEKAY (Customer)

[00:02:35] I started my first class on Thursday as a refresher, so yes and no haha

William S (Tutor)

[00:03:11] OK, no problem! When we factor something out (15x - 10), we're going to basically divide it out of each term.

[00:03:19] So if we want to get rid of 5, we do this:

[00:04:33] Hopefully this diagram makes sense. Basically, we've taken our 5 out so it is by itself on top, then the 5 on the top and the 5 on the bottom can cancel each other out.

CRISTINEKAY (Customer)

[00:04:51] Oh okay

William S (Tutor)

[00:05:40] No matter which method we use to solve this problem, we should come up with the same answer. Do you know what the expression looks like after we simplify it?

CRISTINEKAY (Customer)

[00:06:22] So, it's basically the same (the bottom part) as the one above?

[00:06:38] I'm sorry, I do but don;t understand

William S (Tutor)

[00:06:57] No problem! So those two expressions do equal each other, but they're still not completely simplified.

[00:07:21] To simplify it, we're going to divide both the top and bottom of the fraction by 5, like this:

CRISTINEKAY (Customer)

[00:07:39] Oh all right. I did get as far as the first one 15x over 5 minus 10 over 5 but wasn't sure how to go further

William S (Tutor)

[00:08:51] So (3x - 2) is the simplified version of this expression. It's still equal to (15x - 10)/5, it's just a little easier to make sense of.

[00:09:09] Do you feel like you understand how we arrived at this answer?

CRISTINEKAY (Customer)

[00:09:14] Ohhh..so it is no longer a fraction?

William S (Tutor)

[00:10:13] Right - essentially, what happens is that we divide both the top and the bottom of the fraction by 5. When we do, that leaves us with a 1 on the bottom.

CRISTINEKAY (Customer)

[00:10:15] Yes, I understood how to simplify the expression to get 3x-2, I was just not sure if it still needed to be a fraction because the 5 cancelled itself out.

[00:10:23] I over think these things

William S (Tutor)

[00:10:43] No problem, those are definitely good questions to ask!

[00:11:10] If you're trying to simplify and you can get rid of a fraction (without making another fraction or a decimal), you definitely want to.

CRISTINEKAY (Customer)

[00:11:36] Oh okay, awesome, thank you!!

William S (Tutor)

[00:11:50] Would you like to practice with any other problems, or do you think you've got it?

CRISTINEKAY (Customer)

[00:12:18] I think I'm okay for now, I'm going to write down some notes on it. thanks again William!

William S (Tutor)

[00:12:29] Great! Thanks, and have a great rest of the day!

CRISTINEKAY (Customer)

[00:12:40] thank you, likewise! :)