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.