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# Tutor.com Real Numbers Session

##### Nov. 3, 2016

Session Transcript - Math - MAT104, 10/29/2016 12:23PM - Tutor.com
Session Date: 10/29/2016 12:23PM ET
Length: 40.8 minute(s)
Subject: Math - MAT104

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

Bruce (Customer)
[00:00:00] *** The student has 577 minutes remaining. ***
[00:00:02] I want to practice using PEMA

Christian F (Tutor)
[00:00:13] Hi Bruce. How are you/

Bruce (Customer)
[00:00:21] Hello

Christian F (Tutor)

Bruce (Customer)
[00:01:30] I want to practice more problems using PEMA as I am a beginner to Algebra

Christian F (Tutor)
[00:01:42] Ok. Great.

Bruce (Customer)
[00:02:04] I need to work on the steps

Christian F (Tutor)
[00:02:28] Ok. Do you have a specific problem?

Bruce (Customer)
[00:02:57] no I was hoping you can give me some to practice

Christian F (Tutor)
[00:03:32] Ok. By PEMA you mean parenthesis, exponential, multiplication and addition, right?

Bruce (Customer)
[00:03:40] yes

Christian F (Tutor)

Bruce (Customer)
[00:05:33] ok this looks different from the first problem I solved but let me give it a try
[00:06:23] what is x?

Christian F (Tutor)
[00:06:48] a variable.

Bruce (Customer)
[00:07:17] that is where I get stuck what is a variable

Christian F (Tutor)
[00:07:35] If you haven't seen variables yet, we can remove it from the problem.

Bruce (Customer)
[00:08:07] I haven't I am really a older beginner

Christian F (Tutor)
[00:08:29] Ok, no problem. I will change it.

Bruce (Customer)
[00:09:19] ok the brackets confuse me but let me take a shot at it

Christian F (Tutor)
[00:09:28] ok.
[00:11:36] Is that a 6 in parenthesis?

Bruce (Customer)
[00:11:43] the first step?

Christian F (Tutor)
[00:12:38] I mean in parenthesis, is that (1+6)?

Bruce (Customer)
[00:12:50] yes

Christian F (Tutor)
[00:13:01] Okay. That should actually be 1+8.
[00:13:06] Do you see why?

Bruce (Customer)

Christian F (Tutor)
[00:13:20] Ok.
[00:13:51] Makes sense?

Bruce (Customer)
[00:14:04] yes

Christian F (Tutor)
[00:14:21] So, what is the result of that repeated multiplication?

Bruce (Customer)
[00:15:30] so I also add the 2 = and its 2 x 2 x 2 x 2 =8

Christian F (Tutor)
[00:15:52] Wait. 2x2x2 already equals 8.

Bruce (Customer)
[00:16:24] oh I see 2 x 2 =4 x 2 =8

Christian F (Tutor)
[00:16:31] Perfect.
[00:16:36] Let's write that first.

Bruce (Customer)
[00:17:56] so what about that 2 bracket Im sorry Im confused again

Christian F (Tutor)
[00:18:19] First we do the parenthesis. Then we take care of the bracket.

Bruce (Customer)
[00:18:36] ok

Christian F (Tutor)
[00:19:00] The standard notation is to write parentheses inside, brackets outside, to differentiate htem.

Bruce (Customer)
[00:19:54] like this

Christian F (Tutor)
[00:20:03] But how did the 8 become a 9?

Bruce (Customer)
[00:20:29] 1+8 I thought

Christian F (Tutor)
[00:20:53] Yes, but then there should not be a 1+9 under, but just a 9. makes sense?

Bruce (Customer)
[00:21:31] I guess I dont know when the bracket ends

Christian F (Tutor)
[00:22:10] Okay. But inside the parenthesis there is 1+8 and that just equals 9, correct?

Bruce (Customer)
[00:22:25] yes

Christian F (Tutor)
[00:22:42] Okay, then in the parenthesis below we must just write 9.

Bruce (Customer)
[00:22:59] ok

Christian F (Tutor)
[00:23:02] Great.
[00:23:32] Now we have 9^2. We must do that first before the addition, according to PEMA.
[00:24:08] Wait.
[00:24:20] We must do the 9^2 first.
[00:24:27] We cannot add them like that.

Bruce (Customer)
[00:25:07] ok what does the up arrow mean

Christian F (Tutor)
[00:25:24] raised to the power.
[00:25:56] It basically reads "nine squared", in this case. Makes sense?

Bruce (Customer)
[00:26:28] does that means nine times two

Christian F (Tutor)
[00:26:56] No. Squaring a number means muktiplying it by itself twice. So, 9^2=9x9.

Bruce (Customer)
[00:27:30] ok so thats 81

Christian F (Tutor)
[00:27:34] Great!

Bruce (Customer)
[00:27:54] right

Christian F (Tutor)
[00:28:00] Perfect!
[00:28:10] Now we do the inside the brackets first.

Bruce (Customer)
[00:28:55] 3. 83

Christian F (Tutor)
[00:29:02] 3x83.
[00:29:12] The dot also means multiplying.

Bruce (Customer)
[00:29:19] so . = x ok

Christian F (Tutor)
[00:29:38] Well, the dot I put there is a dot in the center of the line, not a decimal.
[00:30:03] I am not trying to confuse you, it is just a normal convention that you will see in algebra books.

Bruce (Customer)
[00:30:16] ok so the answer is 269
[00:30:25] 249 sorry

Christian F (Tutor)
[00:30:26] 249.
[00:30:29] Perfect!
[00:31:19] Here is a general guideline to solve such problems:

Bruce (Customer)
[00:31:23] how do I practice this I have avoided algebra my whole life now its coming to haunt me

Christian F (Tutor)
[00:32:24] 1- When you write a problem do it from left to right, just as you would write in English. Math is a language and we must have a consistent way of writing it. That helps keeping the problem neat and avoiding mistakes.

Bruce (Customer)
[00:32:45] ok

Christian F (Tutor)
[00:32:45] 2- Do the parenthesis first, starting from the inside and moving outward.
[00:33:23] 3- Do the operations in order and keep the rest intact.
[00:33:48] I can show you how to properly solve this problem if you want, so that you can see how to properly do it.
[00:34:08] ANd you can keep it as a tempate.

Bruce (Customer)
[00:34:10] I need to understand when to end the brackets

Christian F (Tutor)
[00:34:14] Okay.
[00:34:18] Let me show you.

Bruce (Customer)
[00:34:23] ok

Christian F (Tutor)
[00:34:25] Can I redo the problem for you?

Bruce (Customer)
[00:34:33] yes
[00:38:59] ok I think I see it.

Christian F (Tutor)
[00:39:06] See how I re-write the expression from left to write as I would do with english?

Bruce (Customer)
[00:39:14] yes

Christian F (Tutor)
[00:39:18] That is very important in order to not forget things.

Bruce (Customer)
[00:39:35] I see

Christian F (Tutor)
[00:39:44] Also, try to be as neat as possible. Most often students make mistakes because they are sloppy and forget signs or numbers.
[00:39:47] Great.
[00:40:04] Then, the only way to get better at this is to practice as much as you can.

Bruce (Customer)
[00:40:23] Right so I will start working in Aleks thanks

Christian F (Tutor)
[00:40:25] It is really like playing an istrument or playing a sport. The more you practice the better you get at it.
[00:40:32] Anything else?