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System Message

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

Guest (Customer)

[00:00:00] Express the perimeter of the square as a single rational expression.

Sam B (Tutor)

[00:00:07] Welcome to Tutor.com ! How can I help you today?

System Message

[00:00:18] *** Lost connection from Guest (Customer). Waiting for reconnect... ***

Sam B (Tutor)

[00:01:47] From what I see, we have a square of side length 8/(x+3), and are asked to calculate the perimeter as one rational expression.
Is that correct?

Guest (Customer)

[00:01:56] Yes

Sam B (Tutor)

[00:02:12] Cool!
First things first, how do we calculate the perimeter of a square?

Guest (Customer)

[00:02:24] add all the sides

Sam B (Tutor)

[00:02:45] Exactly!
And what's special about the side lengths of a square?

Guest (Customer)

[00:02:53] all the same size

Sam B (Tutor)

[00:03:17] Yup!
So how would we calculate the perimeter in this case if we have a side length of 8/(x+3)?

Guest (Customer)

[00:03:27] multiply it times 4?

Sam B (Tutor)

[00:03:49] Correct!
Since we're adding the term into itself four times, it's the same thing as multiplying it by 4.

[00:04:08] How do we find 4 times 8/(x+3)?

Guest (Customer)

[00:04:35] multiply it to the top and
bottom, right?

Sam B (Tutor)

[00:05:12] Not quite.
Here's another example: Say I have 4 half-dollar coins.
What's the total amount of money I have?

Guest (Customer)

[00:05:47] 2 dollars

Sam B (Tutor)

[00:06:00] Exactly, since 4 times 1/2 equals 2, right?

Guest (Customer)

[00:06:05] yes

Sam B (Tutor)

[00:06:14] So let's write this out:

[00:06:52] If we were to multiply the top AND bottom of the fraction by 4, we'd be left with this:

[00:07:23] And we'd end up with the same amount.

[00:07:51] That's why when we're multiplying a fraction and a whole number together, another way we can write it is like this:

[00:08:13] Since 4/1 is still 4

[00:08:18] Then we just multiply across...

Guest (Customer)

[00:08:29] ok i think im seeing

Sam B (Tutor)

[00:08:42] Does that make sense?

Guest (Customer)

[00:08:54] kind of

[00:09:18] could you show me?

[00:09:24] im sorry .

Sam B (Tutor)

[00:09:38] No problem!
So in the example you have, we're multiplying 8/(x+3) by 4

[00:10:10] So how would this simplify?

Guest (Customer)

[00:10:39] 32 / 4x+12

[00:10:41] ?

Sam B (Tutor)

[00:11:02] You're close!
Let's rewrite the equation so it makes more sense.

[00:11:16] Remember how I changed the 4 into a 4/1, since they were the same number?

Guest (Customer)

[00:11:23] ok

Sam B (Tutor)

[00:11:28] Since any number divided by 1 is itself.

Guest (Customer)

[00:11:38] ok

Sam B (Tutor)

[00:11:48] So would you like to change the equation to show this?

Guest (Customer)

[00:12:20] ?

Sam B (Tutor)

[00:12:29] Right!
Now we just multiply across like this:

Guest (Customer)

[00:12:48] ohh

Sam B (Tutor)

[00:12:51] So we multiply everything in the top part of the fraction by 4, and everything in the bottom by 1.

[00:13:43] Awesome!
And that would be our final answer, since it is written as one rational expression.

[00:13:48] Does that make sense?

Guest (Customer)

[00:13:49] ohh

[00:13:51] yes!

Sam B (Tutor)

[00:13:58] Great job!

[00:14:15] Do you have any other questions or confusion about anything we went over?

Guest (Customer)

[00:14:20] nope

Sam B (Tutor)

[00:14:25] Cool!

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