REAL NUMBERS(LECTURE 2)

REAL NUMBERS_CLASS 10 
(24th March 2020, Tuesday)

LESSON 2

Dear Students,


Yesterday we covered the following learning outcomes:

• recall what are prime numbers and composite numbers 
• write different types of decimal expansions for the real numbers
• state whether given number has terminating or non-terminating decimal expansion 

Let us go through the guidelines for my blog once again:

·         The text in Red, is to be written in your register

·         The text in blue is to be viewed by clicking on it

·         The text in green is to be practiced for home work

·         Follow the instructions (such as write / view / recall....) as and when they appear in my blog

·         I will be with you on this blog from 9:30 am to 10:20 am so that I can address to any queries that you may have when you go through the lesson. However, if you post any query after this, I will address to that only on the next day during the same slot.

1. take your SET-A Mathematics Register
2. Our handwriting reflects a lot about us. It will be awesome if you use good presentation and cursive hand writing
3. Make a column on the right hand side, if you need to do any rough work
4. Leave two lines where you finished yesterday’s work and draw a horizontal line
5. Write today's date on the line after that. We need to save paper. Write the SDG – 12 : Responsible Consumption and Production. Remember we contemplated on SDG-1 in yesterday’s class ? Let us be responsible global citizens. One good thing that Coronovirus is teaching us! That is be responsible global citizens.
6. Pending Queries from yesterday (if any).......
7. Please write the learning outcomes as mentioned below 

I will be able to  :

• Summarise the fundamental theorem of arithmetic
• Generalise relationship between HCF and LCM

Click on the following link to recall how does factorisation work

https://www.mathsisfun.com/numbers/fundamental-theorem-arithmetic.html 

Have you been through the above link ?

If yes then please answer the following questions as Class work right now ?

Q1)   Make 30 by multiplying only PRIME NUMBERS

A1)   30 = ___________________

Q2) How many factors are they ?

A2) ______ (3 / 4 / 7)

Q3)  Ignore the order what you used to answer Q1. Make 30 by multiplying only PRIME NUMBERS using another order.

A3)  30 = ___________________________

Q4)  In Q1 & Q3, have the same prime numbers given you 30, no matter what the order ?

A4)  ______ (Yes / No)

Hope you have answered the above questions !

If not, then here are few hints for you:

** order means , example : (7 * 13 * 2)

** another order means , example : ( 2 * 7 * 13)

Now look at the image given below.  

Please write the Fundamental theorem of arithmetic in your register

Have you observed that you already knew this !

Now, you know it the way Euclid summarised it !

Now let us write few examples using exponents.....life becomes easier. 

Benefits: We take lesser time (remember you need to gear up to write a lengthy CBSE paper!!), chances of errors reduce 

Please look at the image below. It illustrates the steps to do the above. Please take down these examples in your note book.  

Q5) Express each number as a product of its prime factors:

(i)                 150            (ii)      2248

A5) 150 = __________________________

      2248 = __________________________

Hence you should be able to attempt NCERT Ex. 1.2 (Q1 & Q6...refer to yesterday’s lesson for Q6) for home work

Please look at the image below. It generalises the relationship between HCF and LCM. You will need to take a note of this in your note books.

Q6) Find the LCM and HCF of  512 and  68 and verify that LCM × HCF = product of the two numbers

A6) LCM (512, 68) = _______

       HCF (512, 68) = _______

      LHS = LCM × HCF = ______________

      RHS = product of the two numbers = _____________

      HINT : If LHS = RHS , write verified, else check your calculations !

Hence you should be able to attempt NCERT Ex. 1.2 (Q2) for home work 

Please view the example in the video in the link attached below.

https://www.youtube.com/watch?v=SSchuiGVwGQ

Please refer to this video again when you attempt NCERT Ex. 1.2 (Q3) for home work

Please view the example in the video in the link attached below.

https://www.youtube.com/watch?v=a8y1fR9FKiI

Q7) Attempt Q 4 from NCERT ex 1.2

A7) substitute the values in step 1, 2 and 3 and then solve as you have seen in the above video:

      Step -1:   HCF = ____

       Step-2:  LCM × HCF = first number × second number

       Step -3 : LCM = first number × second number

                                                         HCF

Now let us look at Q5 of NCERT ex. 1.2.

Please take this down in your note book

Now you should be able to attempt NCERT Ex. 1.2 (Q7) for home work. 

A worksheet Real Numbers-1 is shared on the whatsapp group. Please spare time to complete this today.

I will begin tomorrow’s class with any queries from the worksheet

That should be all for today !

Good morning and thank you boys !

Take a good care of yourself

See you tomorrow for the next class !