1. Adding integers
without number line
2 digit

2. Integers Recap
Zero
Negative integers
Positive integers
The numbers –1, –2, –3, … (to the left of zero) are called negative integers
The numbers 1, 2, 3,… (to the right of zero) as positive integers.
The new set of numbers …, -3, -2, -1, 0, 1, 2, 3,… are called Integers.
‘–’ symbol in front of a number is read as 'negative' or 'minus'.
For example, –5 is read as negative 5 or minus 5.
A number without a sign is considered as a positive number.
For example, 5 is considered as +5.

3. + ( + ) = + + ( - ) = - - ( - ) = + - ( + ) = -
Rules of Addition and subtraction
Rule 1
Two numbers have same sign
Add the numbers
Copy bigger number sign
Rule 2
Two numbers have different sign
Subtract the numbers
Copy bigger number sign
Rules of multiplication
Converting 2 symbols into 1
Rule 1
Multiply same sign  Answer is +
+ ( + ) = +
- ( - ) = +
Rule 2
Multiply different sign Answer is –
+ ( - ) = -
- ( + ) = -

4. Worked Examples (Using Addition and subtraction rule)
-7 + 3
Numbers have different sign
Using Rule 2 –
Subtract the numbers and copy bigger number sign
7- 3 = 4
Bigger number sign is “ – “
Answer : -4
-7- 3
Numbers have same sign
Using Rule 1-
Add the numbers and copy bigger number sign
7 + 3 = 10
Bigger number sign is “ – “
Answer : -10
7 - 3
Here we can write it as
+7 - 3
Numbers have different sign
Using Rule 2 –
Subtract the numbers and copy bigger number sign
7- 3 = 4
Bigger number sign is “ + “
Answer : +4
+7 +3
Numbers have same sign
Using Rule 1-
Add the numbers and copy bigger number sign
7 + 3 = 10
Bigger number sign is “ + “
Answer : +10

5. + ( + 7 ) + ( - 7 ) - ( + 7 ) - ( - 7 ) +(+)=+ +(-)=- -(+)=- -(-)=+
Worked Examples (Using Multiplication rule)
+ ( + 7 )
+ ( - 7 )
- ( + 7 )
- ( - 7 )
+(+)=+
+(-)=-
-(+)=-
-(-)=+
Answer + 7
Answer -7
Answer - 7
Answer + 7

6. Answer: -33 + 87 = +54 Example 1: Add - 33 + 87 Solution:
Step 1: Check the signs before each integer. Integers should have one sign in front.
Let us take 33, it is having single sign (-) in front. Now take 87 ,it is having one sign
(+) in front.
Step 2: As per Addition rule 2, if the numbers have different sign, subtract the
numbers and copy bigger number sign
87 – 33 = 54 & Bigger number sign is “ + “
Answer: = +54

7. Answer: (-27) + (-36) = - 63 By rule, + ( - ) = -
Example 2: Add (- 27) + (- 36)
Solution:
Step 1: Check the signs before each integer. Integers should have one sign in front.
Let us take 27, it is having single sign (-) in front. Now take 36 ,it is having two signs
(+ & -) in front.
Step 2: By using Multiplication rule, we make it as single sign
Therefore + (-36) = - 36
Step 3: Therefore, (- 27) + (- 36) =
Step 4: As per Addition rule 1, if the numbers have same sign, add the numbers and
copy bigger number sign
= 63 & Bigger number sign is “ – “
By rule, + ( - ) = -
Answer: (-27) + (-36) = - 63

8. Answer: 43 + (-43) = 0 By rule, + ( - ) = - Example 3: Add 43 + (- 43)
Solution:
Step 1: Check the signs before each integer. Integers should have one sign in front.
Let us take 43, it is having single sign (+) in front. Now take second 43 ,it is having
two signs (+ & -) in front.
Step 2: By using Multiplication rule, we make it as single sign
Therefore + (-43) = - 43
Step 3: Therefore, 43 + (- 43) =
Step 4: As per Addition rule 2, if the numbers have different sign, subtract the
numbers and copy bigger number sign
= 0 & ”0” does not have any sign
By rule, + ( - ) = -
Answer: 43 + (-43) = 0

9. Try these
1. Add (- 56)
2. Add 55 + (- 60)
3. Add –