Integers Blog 10

Good Morning Learners,

We are continuing with the chapter 1 Integers. In the previous blogs, you all have learned about

(i) division of integers.
(ii) rules of division of integers.
(iii) formulas of division of integers.

Now we are moving ahead to learn more about 'Properties of Division of Integers'.

Important Instructions:
(i) Red Lines need to be done in your maths note book.
(ii) Green Lines need to be read carefully.
(iii) Keep your text book for reference.
(iv) Home Assignment need to be done in your maths note book.
(v) Complete your index, put chapter name, date, exercise no in your maths note book.
(vi) Important links are provided at the end of the blog for better understanding.

LEARNING OUTCOMES-
At the end of today's topic, learners will be able to
(i) explain the properties of division of integers.
(ii) justify the properties of division of integers.
(iii) solve the problems based on the properties of division of integers.

So let us start the topic of today.......

                                           PROPERTIES OF DIVISION OF INTEGERS

Can you recall the closure property under multiplication. In that property we have discussed that the product of two integers is again an integer. So we can say that integers are closed under multiplication. 
                     a    X    b     =    b   X   a

Now do you all this, will it same in the case of division. Let check it out.....

Observe the table and conclude the inference 

We can easily conclude that integers are not closed under division.

Now, we can discuss the property of division one by one-

1. Division is not Commutative for whole number

Example 1     (- 8 )    ÷  (- 4)    ≠      ( - 4 )    ÷   ( - 8 )

Example 2      (- 9)    ÷   3         ≠      3    ÷    (- 9)

Example 3      (- 30)    ÷    (- 6)   ≠     (- 6 )  ÷   (- 30)    

2. Any Integer divided by zero is meaningless and zero divided by an integer other than zero is equal to zero.   i.e. for any integer  a,               a  ÷  0  is not defined but   0  ÷  a  = 0 for a ≠ 0

Thus, if a is any integer then a  ÷ 0 is not defined.

Example 1           0    ÷   (- 2)   =   0

Example 2          0    ÷    (- 5)  =   0

3. Any integer divided by 1, it gives the same integer.           a   ÷  1  =  a    ;    (- a)  ÷ 1  =  (- a)  

Example 1    (- 8)   ÷   1   =  (- 8)

Example 2    (- 11)   ÷  1  =  (-11)

Example 3    (-48)    ÷   1  =  (- 48)

By this we end the properties of division of integers. I hope you all will be able to solve the problems given exercise 1.4 of chapter 1. 

For more information click on the link : https://www.youtube.com/watch?v=0-tksHOvW40
                   
                                                                https://www.youtube.com/watch?v=b6JaiKvEP9Y&t=182s

                                                                https://www.youtube.com/watch?v=o1FcE65VYzM

But let me help you all to solve few questions of this exercise 1.4

Q5. The temperature at 12 noon was 10 ℃ above zero. If it decreases at the rate of 2 ℃ per hour until midnight, at which time would the temperature be 8 ℃ below zero? What would be the temperature at mid-night?

A5. Have a look on the number line

The temperature decreases 2 ℃  = 1 hour, the temperature decreases 1℃  = 1/2 hour

The temperature decrease 18 ℃= 1/2  X  18 = 9 hours

Total time = 12 noon + 9 hours = 21 hours = 9 pm


Thus, at 9 pm the temperature would be 8℃ below 0℃.

Q6.  Read the question from your text book.
A6. (i) Marks given for one correct answer = 3
            Marks given for 12 correct answers= 3 X 13 = 36
            Radhika scored 20 marks.
            Therefore, marks obtained for incorrect answers= 20 - 36 = -16
            Now, marks given for one incorrect answer = - 2
            Therefore, number of incorrect answers = (- 16)  ÷  (- 2) = 8
            Thus, Radhika has attempted 8 incorrect questions.

     (ii) Marks given for seven correct answers = 3 X 7 = 21
           Mohini scores  =  -5
           Marks obtained for incorrect answes = -5 -21 = -26
           Now, marks given for one incorrect answers = -2
           Therefore, number of incorrect answers= (- 26) ÷ (- 2)= 13

           Thus, Mohini has attempted 13 incorrect questions.

Q7. Read question for your text book.
A7. When starting position of mine shaft is 10 m above the ground but it moves opposite direction so it travels the distance (- 350 m ) below the ground.
       So total distance covered by mine shaft = 10 m - (- 350) m = 10  +  350 = 360 m
       Time taken to cover the distance of 6 m by it = 1 minute   
So, time taken to cover a distance of 1 m by it = 1/6 minutes
Terefore, time taken to cover a distance of 360 m = 1/6  X  360  = 60 m = 1 hour
Thus, in one hour the mine shaft reaches -350 m below the ground.

HOME ASSIGNMENT
1. Complete Ex 1.4 of your text book.
2. Do neat and clean work.