Integer rules:

Integer rules are the key to do operations with integers and later on solving problems in algebra.


To understand integer rules, students should be clear on the basic concepts of integers. students have to give up the habit to consider the positive or negative signs between two numbers. They need to learn that all the numbers have their signs (positive or negative) at left front of them as explained in the previous lesson.


Integer rules on adding and subtracting integers


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Recall:


Same signs add and keep, add and keep.


Opposite signs you subtract, take the bigger number sign then you are exact.


Keeping above rules in mind, we go further for the integers hunt. You have learned basic integer rules, how to adding and subtracting integers. In this lesson, you are going to learn both operations together, that is adding and subtracting integers, and use of the parenthesis or brackets with the integers.


Open brackets or parenthesis “(  )” are often used to create integer problems more complex. There are good integer rules to deal with the parenthesis. The method you are learning in this lesson is the simplest of all the other methods.


You just need to open or solve the brackets before you apply the integer rules. The rules to open the brackets are explained below:


1) To open a bracket with the negative sign in front of it, open the bracket by changing the sign of the number in the bracket. For example;


   - (3) = -3        - (-3) = +3 or 3   

     

   - (5) = -5         - (-5) = 5


2)   If there is a positive sign in front of a bracket, open the bracket without changing the sign of the number in the bracket. For example;


+ (3) = 3            + (-3) = -3 

        

+ (5) = 5            + (-5) = -5



In summary, negative sign in front of a bracket changes the sign of the number in the bracket when bracket is opened.


Positive sign in front of the bracket does not change the sign of the number in the bracket, when bracket is opened.


Simplify the following to better understand the integer rules on adding and subtracting integers:


1)   – (4) – (8)


2)   3 + (-9)


3)   7 – (-5)


4)   – 6 – (-2)


5)   – (- 9) – (+11)




Solutions:


1)   – (4) – (8)  

 

Both brackets got negative signs at front and both numbers 4 and 8 inside the brackets are positive. So, change the signs of both the numbers to minus and open the brackets. 

      

= - 4 – 8   


Same signs add and keep. 


= -12  



               

2)   3 + (- 9)


There is only one bracket and has “plus” sign in front of it. So, open this bracket without changing the sign of the number inside, that is -9 stays -9 after opening the bracket as “plus” sign opens the brackets without changing the sign of the number inside the bracket.


= 3 – 9


Opposite signs you subtract, keep the bigger number sign then you are exact!

 

= - 6




3)   7 – (- 5)


There is only one bracket having “minus sign” at front. So, open this bracket by changing the sign of the number inside. Therefore change – 5 to +5 and open the bracket.


= 7 + 5


Same signs add and keep.


= 12




4)   – 6 – (- 2)


There is only one bracket again having “minus sign” at front. So, open this bracket by changing the sign of the number inside. Therefore change – 2 to +2 and open the bracket.


= - 6 + 2


Opposite signs you subtract, keep the bigger number sign then you are exact!


= - 4




5)   – (- 9) – (+11)


Both the brackets have the negative signs at front. So, open the brackets by changing the signs of the numbers inside the brackets.


Therefore, change – 9 to +9 and +11 to – 11.


= 9 – 11


Opposite signs you subtract, keep the bigger number sign then you are exact!


= -2




More examples on adding and subtracting integers:


i) - 5 + (- 6)


= - 5 – 6    [As + (-6) = -6]


= -11        [Same signs add and keep]




ii) – (- 12) – (+10)


= 12 – 10       [As – (-12) = +12 or 12 and – (+ 10) = - 10]


= 2        [Opposite signs you subtract, and keep……]




iii) (- 25) + (- 25)


= - 25 – 25


= - 50




There is another method which keeps the two signs together. What I found that brackets and two signs together make students confused and they make more mistakes. Therefore, students should get rid of any brackets or double signs, before they move to apply the integer rules. There are some more examples on double signs to understand further adding and subtracting integers:


i)  - 9 - - 11


= - 9 + 11      [Remember that, - - = +]


= 2




ii) 6 + - 15


= 6 – 15     [Remember that, + - = - or - + = -]


= -9




iii) - - 17 - + 20


= 17 – 20


= -3


This is all about adding and subtracting integers. You have learned the rules to add and subtract the integers including brackets and doubles signs.


Follow the integer rules given in the lessons and you will never struggle in adding and subtracting integers again.