RATIONAL NUMBERS(LECTURE 4 )

RATIONAL NUMBERS      

LESSON 4

Welcome you all once again!

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 BLUE, is to be written in your register

·         The text in Red 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

 ADDITION, SUBTRACTION , MULTIPLICATION AND DIVISION OF RATIONAL NUMBERS 

 WHAT ARE RATIONAL NUMBERS ?

click on  the link Rational numbers Rational numbers are the numbers which can be represented in the form of p/q, where q is not equal to 0.  Let us go through all the properties here.

Properties of Rational Numbers

The major properties of rational numbers are: Closure Property Commutative  Property Associative Property Distributive Property

Today ,let us  study Closure  and Commutative property  in detail.

Closure Property

                                                            click on link

1) Addition of Rational Numbers

The closure property states that for any two rational numbers a and b, a + b is also a rational number.
1/2 + 4/2
= ( 1 + 4) /2
= 5 / 2

The result is a rational number. So we say that rational numbers are closed under addition.

2) Subtraction of Rational Numbers

The closure property states that for any two rational numbers a and b, a – b is also a rational number.
1/2 - 4/2
= ( 1 - 4) /2
=  -3 / 2
The result is a rational number. So the rational numbers are closed under subtraction.

3) Multiplication of Rational Numbers

The closure property states that for any two rational numbers a and b, a × b is also a rational number.
1/2   ✕ 4/2                 = (1  ✕   4) /  ( 2 ✕  2 ) = 4 / 4   = 1 / 1
The result is a rational number. So rational numbers are closed under multiplication.

4) Division of Rational Numbers

The closure property states that for any two rational numbers a and b, a ÷ b is also a rational number
1/2    ➗ 4/2             = (1 x 2)  /  ( 2 x 4  =    2/8 = 1/4 .
The result is a rational number. But we know that any rational number a, a ÷ 0 is not defined. So rational numbers are not closed under division. But if  we exclude 0, then all the rational numbers are closed under division. Commutative Property

click on the  link

1. Addition

For any two rational numbers a and b, a + b = b+ a
1/2 + 4/2  =  (1 + 4) / 2  = 5 /2
4/2 + 1 /2  =  (4 + 1) / 2  = 5 /2

We see that the two rational numbers can be added in any order. So addition is commutative for rational numbers.

2. Subtraction

For any two rational numbers a and b, a – b ≠ b –  a.  Given are the two rational numbers 1 / 2 and  4/2 1/2  -  4/2  =  (1 - 4) / 2  =  -3 /2
 But 4/2 -  1 /2  =  (4  -  1) / 2  = 3 /2 So subtraction is not commutative for ratioanl numbers.

3. Multiplication

For any two rational numbers a and b, a × b = b × a 1/2   ✕ 4/2                 = (1  ✕   4) /  ( 2 ✕  2 ) = 4 / 4   = 1 / 1 And     4 / 2   ✕ 1 / 2                 = (4  ✕  1 ) /  ( 2 ✕  2 ) = 4 / 4   = 1 / 1
We see that the two rational numbers can be multiplied in any order. So multiplication is commutative for rational numbers.

4. Division

For any two rational numbers a and b, a ÷ b ≠ b ÷ a. Given are the two rational numbers 1/2    ➗ 4/2             = (1 x 2)  /  ( 2 x 4  =    2/8 = 1/4 But  4 / 2    ➗   1 / 2             = (4 x 2)  /  ( 2 x 1  =    8  / 2 = 4     We see that the expressions on both the sides are not equal. So division is not commutative for rational numbers.

Exercise  1.1  (TO BE DONE IN Maths REGISTER)

Question 5:

Name the property under multiplication used in each of the following:
(i) 
(ii) 

ANSWER:

(i) 
(ii) Commutative

Question 6:

Multiply by the reciprocal of.

ANSWER:

LETS PRACISE



 Q1.Verify that:.(i)        and  are  same                                           are same   

 Q2.  Find:             

 Q3.   What should be added to -16/3 to make it 1/9?

 Q 4. What should be subtracted from 5/8 to make it -1?

We have double period today, so you can practice more sums on the same topic from NCERT text or any other book available to you .

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