Intergers Blog 9

Good Morning Learners,

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

(i) Numbers, Positive and Negative Integers
(ii) Properties of Addition and Subtraction of Integers
(iii) Multiplication of Integers

Now we are moving ahead to learn more about '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 division as the inverse operation of multiplication.
(ii) justify the division as the inverse operation of multiplication.
(iii) solve problems of division of integers.

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

                                                       DIVISION OF INTEGERS

Look at the examples for whole numbers-

Example 1:                 3   X   5   =  15

when we divide 15 by 5    (15  ÷ 5 =  3)  In the same way when we divide 15 by 3  (15  ÷  3  =   5)

Example 2:                4     X    3  =   12

when we divide 12 by 4  (12  ÷  4  =  3)     In the same way when we divide 12 by 3  (12  ÷ 3 =  4)

Example 3:              6      X      4  =  24

when we divide 24 by 6   (24  ÷  6  =  4)  In the same way when we divide 24 by 4   (24   ÷  6   =  4)

Example 4:                 7    X    5    =  35

when we divide 35 by 7 (35  ÷ 7  =  5)   In the same way  when we divide 35 by 7 ( 35 ÷ 5 = 7)

These examples proves that "MULTIPLICATION STATEMENT OF WHOLE NUMBERS THERE ARE TWO DIVISION STATEMENTS"

The operation of division is an inverse operation of multiplication. 

If a and b are two integers (a and b not equal to 0), then dividing a by b is same as finding an integers c which when multiplied by b gives a 

                 b    X    c   = a
    
thus,        a   ÷   b  = c  is same as    b    X    c   =   a

TASK 1: Observe the following table where in column A is multiplication statement and column B is corresponding division statements. 
One is done for you all, help your self in complete the rest

Now, let us all see the division of integers. For better understanding observed the following examples-

Now, we should learn about Divisions of Integers.

Example 1     (-12)  ÷  3   =  - 4

Example 2     (-12)  ÷  2    =  - 3

Example 3    (-32)   ÷  4    =   - 8

RULE:  when a negative integer is divided by a positive integer, divide the numbers as whole numbers and put a negative sign before the quotient to get a negative integer.

Example 4     72   ÷  (-8)   = - 9

Example 5     50   ÷  (-10)  = - 5

Example 6     72   ÷   (-9)   = - 8

RULE: when a positive integer is divided by a negative integer, divide the number as whole numbers and put a negative sign before the quotient to get a negative integer.

FORMULA:            For any two positive integers a and b; where b is not equal to 0

                                  a   ÷   (- b)   =  (-a)  ÷   b                   where b is not equal to 0

RULE: when a negative integer is divided by a negative integer, divide the number as whole numbers and put a positive sign before the quotient to get a positive integer.

FORMULA:          For any two positive integers a and b; where b is not equal to 0

                                 (-a)  ÷   (-b)   =    a  ÷  b              where b is not equal to 0   

TASK 2: Observe the following table where in column A is multiplication statement and column B is corresponding division statements. 
One is done for you all, help your self in complete the rest.

Information Links:  (1)  https://www.youtube.com/watch?v=b6JaiKvEP9Y

                                 (2) https://www.youtube.com/watch?v=AsRIuvKzvfo

                                 (3) https://www.youtube.com/watch?v=zwDnnSANoQU

HOME ASSIGNMENT:
1. Do "Try These" on page 23.
2. Do Q No 1, 2, 3 of  Exercise 1.4