RATIONAL NUMBERS(LECTURE 5)

RATIONAL NUMBERS 

LESSON 5     

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

Yesterday we covered the following learning outcomes:

Recall  

.1.closure property

2.commutative  property

3.Associative Property

Take any three rational numbers a, b and c. Firstly add a and b and then add c to the sum. (a + b) + c. Now again add b and c and then a to the sum, a + (b + c). Is (a + b) + c and a + (b + c) same? Yes and this is how associative property works.
         (a + b) + c = a + (b + c) 

 It states that you can add or multiply numbers regardless of how they are grouped.

click on this link given below:-

Associative property

For example, given numbers are 5, -6 and 23
( 5 – 6 ) + 23
= -1 + 23
= – 13
Now, 5 + ( -6 + 23 )
=  – 13

In both the groups the sum is the same.

• Addition and multiplication are associative for rational numbers.
• Subtraction and division are not associative for rational numbers.

4.Distributive Property

click on this link 

Distributive property

Distributive property states that for any three numbers x, y and z we have

  x × ( y + z ) = (x × y) +( x × z)

Exercise 1.1  ( Q7 to Q 11)  TO BE DONE IN MATHS REGISTER

Question 7:

Tell what property allows you to compute.

ANSWER:

Associativity
Question 8:

Isthe multiplicative inverse of? Why or why not?

ANSWER:

If it is the multiplicative inverse, then the product should be 1.
However, here, the product is not 1 as

​​​​​​​​​​​​​​​​

Question 9:

Is 0.3 the multiplicative inverse of? Why or why not?

ANSWER:

0.3 ×  = 0.3 × 
Here, the product is 1. Hence, 0.3 is the multiplicative inverse of

Question 10:

Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.

ANSWER:

(i) 0 is a rational number but its reciprocal is not defined.
(ii) 1 and −1 are the rational numbers that are equal to their reciprocals.
(iii) 0 is the rational number that is equal to its negative.
Question 11:

Fill in the blanks.
(i) Zero has __________ reciprocal.
(ii) The numbers __________ and __________ are their own reciprocals
(iii) The reciprocal of − 5 is __________.
(iv) Reciprocal of, where is __________.
(v) The product of two rational numbers is always a __________.
(vi) The reciprocal of a positive rational number is __________.

ANSWER:

(i) No
(ii) 1, −1
(iii) 
(iv) x
(v) Rational number
(vi) Positive rational number
LET'S PRACTICE    (home work)  
Q1. Name the property of multiplication illustrated by the following statements:

(i) -11/13 × -17/5 = -17/5 × -11/13

(ii) {(-2)/3 × 7/9} × (-9)/5 = (-2)/3 × {7/9 × (-9)/5}

(iii) (-3)/4 × {(-5)/6 + 7/8 = {(-3)/4 × (-5)/6} + {(-3)/4 × 7/8}

Q2. Verify the following rational numbers using the multiplication properties:

(i) 3/7 × {5/6 + 12/13} = (3/7 × 5/6) + (3/7 × 12/13)

(ii) -15/4 × (3/7 + (-12)/5) = (-15/4 × 3/7) + (-15/4 × (-12)/5)

(iii) (-8/3 + -13/12) × 5/6 = (-8/3 × 5/6) + (-13/12 × 5/6)

(iv) -16/7 × {-8/9 + (-7)/6} = (-16/7 × (-8)/9) + ((-16)/7 × -7/6)