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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PRACTICE WORKSHEETS

BODMAS WORKSHEET LEVEL1

BODMAS WORKSHEET LEVEL2 

BODMAS WORKSHEET LEVEL3

BODMAS WORKSHEET STD 6th 

BODMAS WORKSHEET STD 7th

RULE OF SIGN ADDITION WORKSHEET

What is BODMAS?| VBODMAS rules and order of operations | how question is solved using BODMAS ?| BODMAS examples

 What is BODMAS?

The BODMAS is an acronym to help students remember the orders of mathematical operations like we generally give a name to something just to remember it for longer time.

VBODMAS  stands for -->

                  V - Vinculum

                  B - Brackets

                  O - Order(order includes powers,percentage,parts"of" etc)

                  D - Division

                  M - Multiplication

                  A - Addition

                  S - Subtraction

**NOTE:- we will learn about Vinculum once we understand other parts of it.(only BODMAS).

whenever we have to perform some mathematical operation involving combination of many operators we use BODMAS method to simply our problem.

according to this method we have to solve the "bracket" first den solve all the "indices then do "division/multiplication" and finally "addition/subtraction'

Note: here the rank of (division and multiplication) is equal also the rank of (addition and subtraction)is equal.

now what is mean by equal rank, let us understand with an example

       ex:- 2+3-1=?

here in this sum we have to perform two mathematical operations

lets we first do addition - step1           2+3=5

now in the result of step1 i.e;   subtract 1

                       step2            5-1=4   --answer1

 in this step perform subtraction first

                        step1            3-1=2   

now in result of step1 i.e; 2, add 2

                        step2            2+2=4   --answer2

here if we look at both the answers they are coming same, means we can either perform addition first followed by subtraction or we can do subtraction first followed by addition.

same goes with multiplication and division too. that is we can multiply the numbers first followed by division and vice versa.

let us see an example for this too 

hope this small step is clear to you. yippieee!!!!! we have done it so easily.now many of you must be thinking if both the operators are of equal ranks then how should we go about to perform these operations??

let me tell you a simple RULE ----- 

always go from "LEFT to RIGHT"

                                         

let us see with an example

                            6÷2×6 

                 solve this by left to right 

                ✅           6÷2=3

                            3×6=18   ---1

          

             now solve it by right to left

                        

               ❌              2×6=12

                             6÷12=0.5   ---2

here we can see that both the answers are different for same question so we need to keep this in mind that no matter what we have to solve the question from LEFT to RIGHT only.

we have understand it till here,lets solve some questions to have good practice.------>  WORKSHEET LEVEL1

 i am doing one for you

                  ex:-  2×6+6......here in this which part is calculated first? 

as per BODMAS of  both the operators, "multiplication"is performed before"addition".   

 so                    2×6+6  =  12+6  =  18.

also solve these questions  🠚      1) 12−8+2  

                                                  2) 12+8×2

                                                  3) 15−3×4

                                                  4) 8÷2×4

LEVEL1 SUCCESSFUL

now we will see some more questions which include bracket and indices

    ex:-  (15−3)×4

here if we look in BODMAS 1st word is 'B' that means first bracket will be solved( i.e; subtraction of 15 and 3) followed by multiplication with 4. so lets solved it

           (15-3) =12 ===>12×4 = 48 

   ex:-  (12+8)×2

           (12+8) = 20 ===>20×2 =40

lets us take one more example

    ex:- (3+5)×6−2×(3×4)

here we have two brackets so we can simultaneously solve both the brackets i.e;  step 1 ->  (3+5) = 8      and      (3×4) = 12

             8×6−2×12  

now after bracket as there is no indices so next priority is multiplication/division. here two multiplications are given so we can solve both simultaneously.

                     step 2 ->   8×6 = 48      and       2×12 = 24

                     step 3 ->     48-24 

now we will see an other example

    ex:- (3²+5)×4−4

here in this question as per BODMAS we will solve bracket first but within bracket also there are two operators one is square and other is addition. square is one of the indices.so again within the bracket we will apply BODMAS. according to that indices should be solved first and then addition.

          step 1  -> (3²+5) ==> 3×3+5 = 9+5 = 14 

          step 2 -> 14×4−4 ==> 56-4 =52

I hope these examples would have helped you.for more practice solve this WORKSHEET LEVEL2. 

Understood till here?

let us see some more complex examples to ace this concept.

===>  ((15−3)×2÷ 25% of 12)

         

          in this question we will first solve bracket

          (15-3)=12

now we will solve percentage (as percentage is same rank as of indices)

           25% of 12 = 3   if you don't know how to calculate percentage you can refer PERCENTAGE.

        let us rewrite it

        12×2÷3

        now for this, we will go for left to right (multiplication and division are of same rank)

        24÷3 = 8

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