subject: Operations With Integers - 3 [print this page] So far you have learned how to add and subtract integers in the previous articles on integers. Recall from the previous articles;
i) Same signs add and keep, add and keep.
ii) 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 integers, how to add and subtract integers in the previous three articles on integers. In this article, you are going to learn both operations together 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 many methods to deal with the parenthesis. The method you are learning in this article is the simplest of all.
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) If there is a negative sign in front of a bracket, open the bracket by changing the sign of the number in the bracket. For example;
- (3) = -3 and- (-3) = +3 or 3 also - (5) = -5 and - (-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;
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:
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:
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
Some books keep 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:
i)-9 - - 11
= -9 + 11 [Remember that, - - = +]
= 2
ii)6 + - 15
= 6 15 [Remember that, + - = - or - + = -]
= -9
iii) - - 17 - + 20
= 17 20
= -3
That's all about adding and subtracting integers. You have learned the rules to add and subtract the integers including brackets and doubles signs. Follow the rules given in the articles and you will never struggle in integers again. There are more methods to deal with the same examples given here. But the given methods are chosen because most of the students liked and understood these methods easily. You will find multiplication and division rules on integers in my coming articles.
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