RATIONAL NUMBERS(LECTURE 6)

RATIONAL NUMBERS      LESSON 6

GOOD MORNING STUDENTS!!!!!!!!!

Few Instructions: 

1. Note down  the work in your register on a regular basis.

2. Notify me about  your presence in the class  as soon as you join, in the comment section. Just  write " Good Morning" along with your name .

3. AS ALREADY MENTIONED,YOU CAN USE ANY NOTEBOOK AVAILABLE AND SUBMIT SEPARATELY ONCE THE SCHOOL REOPENS.4.

4. Take your SET-A Mathematics Register

5.Our handwriting reflects a lot about us. It will be awesome if you use good presentation and cursive hand writing

6. Make a column on the right hand side, if you need to do any rough work

7.Write today's date.

Guidelines for the Blog

·         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

·         Feel free to clarify your doubts by dropping a comment before going ahead in the lesson

QUICK REVIEW OF  PREVIOUS  CLASS

WHAT ARE RATIONAL NUMBERS ?

Rational numbers are the numbers which can be represented in the form of p/q, where q is not equal to 0. 

You are now  familiar with major properties of rational numbers such as :Closure Property, Commutative  Property, Associative Property ,Distributive Property.

Write down today's learning outcomes: 

I will be able to use the concept of   (i)Role of zero      (ii) Multiplicative Inverse.

Let us now see:

 Is 0 included in rational numbers?                                                                           

Yes, 0 is a rational number. The definition of a rational number is a rational number is a number of the form p/q where p and q are integers and q is not equal to 0.

 Examples of rational numbers are 3/5, -7/2, 0, 6, -9, 4/3 etc. It can be seen 0 is a rational number equal to 0/1, 0/5, 0/15, ..etc.

Click the link to learn the ROLE OF ZERO

https://www.youtube.com/watch?v=MzMD2-XLNYQ

What do you observe? You will find that when you add 0 to a rational number, the sum is again that rational number. This happens for  integers and  whole numbers as well.
a +0 =  0 +a  =a,          where a is a rational number
b +0 = 0+ b = b,            where b is an integer
c+0 =0 +c =c,                 where c is a  whole number.
Zero is called the additive identity or the identity element  for the addition of rational numbers. It is the additive identity for integers and whole numbers as well .
For Example:(do it in the register)
(i) 7/8 + 0 = 7/8 + 0/8 = (7+0)/8 = 7/8.
(ii) 0 + 17/-18 = 0/18 +-17/18 = (0-17)/18 = -17/18.

Negative of a rational number: If a/b is a rational number , then –a/b is a rational number such that a/b +[-a/b] = [-a/b] + a/b = 0. -a/b is called negative of a/b. It is also called the additive inverse of a/b. Then a/b is the  negative of –( a/b), i.e., a/b = -[-a/b] We have 0+0 = 0 = 0 + 0, so 0 is the only rational number which is its own additive inverse.

Class Work

Write the additive inverse of the following:
(i) 3/7            (ii) -14/19             (iii) 9/-16                 (iv) -21/-40

Fill in the blanks:
(i) The sum of a rational number and its additive inverse is ..................... (ii) .................is its own additive inverse. (iii)The additive inverse of -21/-30 is ............... You have seen the role of 1 also in the above video, when you multiply any rational number with 1, you get back that rational number as the product. that is  a x 1 = 1 x a = a for any rational number a. therefore , we can say that 1 is the multiplicative identity for rational numbers.  
  

Existence of multiplicative inverse: Every non- zero rational number a/b has its multiplicative inverse b/a. Thus , [a/b x b/a] = [b/a x a/b] = 1. b/a is called the reciprocal of a/b. It is denoted by [a/b]-1 . Thus, [a/b]-1 = b/a. The reciprocal of zero does not exist. Reciprocal of 1 is 1 and the reciprocal of (-1) is -1.

Examples: The reciprocal of 15 is 1/15, of -3 is -1/3 and of (1/8) is 8.

Test your understanding:

Which two properties of multiplication are involved if we wish to show that  5 x 1/5 a = a ?

Are you ready  to verify - (-x) is the same as x = 13/17.
Solution: we have  x  = 13/17 The additive inverse of  x = 13/17 is -x = -13/17 since 13/17 + (-13/17) = 0.
The same equality 13/17 + (-13/17) = 0, shows that the additive inverse of -13/17 is 13/17 or -[-13/17] = 13/17, i.e., -(-x)  = x.

Home Work

Attempt these: 
(i) State True / False     a. -3/17 x 0 = -3/17     b. 6/35 ➗ 0 = 0     c. [p/q] x[p/q]^-1    =1

(ii) State the multiplicative inverse of [-4/5]

^{(iii)State the reciprocal of 9/-19 (iv)Find the sum of the additive inverse and multiplicative inverse  of 2.} 


  

AQAD:

The product of two rational numbers is  If one of them is  then find the other:

That's all for today

Good morning and thank you children

See you all after Easter break!!!