RULE OF SIGN | HOW OPERATIONS ARE PERFORMED ON NEGATIVE NUMBERS? | ADDITION,MULTIPLICATION OF NEGATIVE NUMBERS .

 Are you still confused how to perform the mathematical operations like Addition,Subtraction,Multiplication and Division ??  you often mistake in assigning the results of these operation. 

you have reached to a right place, here we are going to learn the rule for different operations separately and after this you will not have any doubts left.
so let us proceed......

before going to rules let us understand few terms

• SIGN -----> sign are of 2 types

1. Positive (+)

1. Negative (−)   

• NUMBERS ---->  here we are seeing only 2 types of numbers

1. Positive number (number having + sign)

1. Negative number (number having − sign)

• OPERATIONS---> there are 4 types of basic operations mathematics.

Addition
Subtraction
Multiplication
Division
Now we will proceed towards our rule ,our first RULE is for Addition

RULE FOR ADDITION

1. If both the numbers are same i.e; both are positive numbers or both are negative numbers -----> same sign as of numbers (Add the numbers)

1. If both the numbers are opposite i.e;one is positive number and other is negative number -----> sign of greater number (Subtract the numbers)

now let us understand the rule
     if we have two numbers having same sign  ex:- 3 and 5, here both the numbers are positive and we have to add the numbers
 3+5=8,  here we simply added the numbers and put the sign as"+" because here both the numbers are positive
lets see another example
(−2)+(−5)= −7,   here as both the numbers are negative number so we simply added the numbers and put the sign as "−" because both the numbers have negative sign.

--> now we will understand 2nd rule with an example

ex  (−2)+(5)= 3,  here as both the numbers are opposite i.;e 2 is a negative number and 5 is a positive number.so according to 2nd rule we subtracted the numbers and put the "+" sign before the result because our rule says the sign will be same as of the greater no.

lets take another example
ex  1+(−4)= −3,   here as both are opposite numbers so we subtracted it and then put "−" sign before the result because in this the greater number is 4 which is negative.

RULE FOR SUBTRACTION

  rule for subtraction is very simple, ere we have only two steps to perform

•  Step 1 → convert the subtraction into addition.

  now question arises how to convert?? we have to do 2 things here

if sign of the 2nd number is opposite to subtraction sign"−" i.e; "+", simply swap the signs, our aim to do this is just to have addition between two the numbers. 

if sign of the 2nd number is same i.e; "−", just put "+" sign at their place.

  let us see what does it mean
ex  (5)-(2),  here sign of 2nd number is positive(+) which is opposite to subtraction sign "−" so we will swap the sign as ------(5)+(−2)

 here we have addition of two numbers 
ex (5)−(−2),  here sign of 2nd number is negative(−) which is same as subtraction sign"−" so we will  put "+" sign between them

   (5)+(2) and here we have addition of two numbers, our purpose is achieved.

•  Step 2→  now do the addition of numbers as we have learnt it already.

now we will see some examples for subtraction.
 
       (2)−(−5)=           2+5 =                      7

                                  
   same sign,put '+' between them           add it using rule for addition

 ex  (−2)−(4) =   (−2)+(−4) =      −6

      

add it using rule for addition

                               

 

some more examples

 (9)−(4)=   9+(−5 )=     4

 (9)−(−4)=   9+4 =     11.

RULE FOR MULTIPLICATION

1. If both the numbers are same i.e; both are positive numbers or both are negative numbers====> always "+" (Multiply the numbers).

1. If both the numbers are opposite i.e; one is positive number and other is negative number====> always "−" (Multiply the numbers).

     if we have two numbers having same sign  ex:- 3 and 5, here both the numbers are positive and we have to multiply the numbers and put "+" sign with the result.
         3×5=15

ex 1     (−2)×(−6)=12,   both the numbers are negative, so multiply it and put "+" sign with result.

ex 2    2×(−6)= −12,  one no. is positive and other is negative, so multiply it and put "−" sign with result.

RULE FOR DIVISION

1. If both the numbers are same i.e; both are positive numbers or both are negative numbers====> always "+" (Divide the numbers)

1. If both the numbers are opposite i.e; one is positive number and other is negative number====> always "−" (Divide the numbers)

     if we have two numbers having same sign  ex:- 15 and 5, here both the numbers are positive and we have to divide the numbers and put "+" sign with the result
         15÷5=3 
ex1    (−15)÷(−3)=5 ,   both the numbers are negative, so divide it and put "+" sign with result.

ex2    15÷(−3)= −5 ,  one no. is positive and other is negative, so divide it and put "-" sign with result.

finally we have understood the rule of sign for different operations, I hope you would like it.

 for more practice questions refer WORKSHEET.


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