REAL NUMBERS (LECTURE 6)

Lesson 6

Dear Students,

Good Morning Everyone!!

Yesterday we covered the following learning outcomes:

1 recall what is Euclid's Division Lemma

2  recall what is Euclid's Division Algorithm.

3.  recall difference between  Euclid's Division Lemma and  Euclid's Division Algorithm.

Let us go through the guidelines for the  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

•              I will be with you on this blog from 10:30AM____ till 11:20AM____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

1.     Leave two lines where you finished yesterday’s work and draw a horizontal line

2.     Write today's date on the line after that. We need to save paper. Write the SDG – 12  Remember we contemplated on SDG-17 in yesterday’s class ? Let us be responsible global citizens. One good thing that Coronovirus is teaching us! That is be responsible global citizens.

3.     Pending Queries from yesterday (if any).......

4.     Please write the learning outcomes as mentioned below 

   I will be able to summarize:
 Euclid's Division  Lemma  
  To find HCF of two numbers using Euclid's division Algorithm                          

                                                                                                                                            et             Recall Euclid's Division  Lemma                                                                                                                                                                                                      
       Given two positive integers 'a' and 'b', there exists a unique pair of integers q and r such that                                                        
                 a =   b x q   + r,     0   ≤    r  <  b                                                                                                                                                                                                                                                Lets solve an  example:-

1.Show that every positive integer is of the form 2q and that every positive odd integer is of the form 2q +1.

SOLUTION
let a  be any positive integer and b = 2
Then ,by  Euclid's Division  Lemma  , we have 
a = 2q +r   where   q ≥ 0  and     0   ≤    r  <  2
  then a = 2q + r , where r = 0 , 1
When r = 0  ,  a = 2q + 0       => a is an even  integer
When r = 1    , a = 2q + 1      => a is an odd  integer  .
Hence every positive even integer is of the form 2q and evevy positve odd integer is of the form 2q + 1.

Now  look at the image for the solution of Ex 1.1 Q2

 Now  look at the image for the solution of Ex 1.1 Q4
 Que 4:  Show that square of  any  positive interger is either the form  3m or  3m +1 for some integer m.

SOLUTION:-

 Now  look at the image for the solution of Ex 1.1 Q5

A quick review of the chapter 1 Real Number

IMPORTANT: ( Answer   this question in the comment column)

EDUCATION IS WHAT REMAINS AFTER ONE HAS FORGOTTEN WHAT ONE HAS LEARNED IN SCHOOL ............................Albert Einstein 

  SDG 4     QUALITY EDUCATION

So set your GOALS and work hard to achieve it!! 

REAL NUMBERS TEST ON 01/04/2020

PREPARE WELL & ALL THE BEST

Today’s  lesson  ends here!!

Have a good day and take care