1. subtracting integers
without number line
3 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: - 110 - (- 168) = + 58 By rule, - ( - ) = +
Example 1: Subtract ( )
Solution:
Step 1: Check the signs before each integer. Integers should have one sign in front.
Let us take 110, it is having single sign (-) in front. Now take 168 ,it is having two
signs (- & -) in front.
Step 2: By using Multiplication rule, we make it as single sign
Therefore - (- 168) = + 168
Step 3: Therefore, (-168) =
Step 4: As per Addition rule 2, if the numbers have different sign, subtract the
numbers and copy bigger number sign
= 58 & Bigger number sign is “+“
By rule, - ( - ) = +
Answer: (- 168) = + 58

7. Answer: 250 - (- 349) = + 599 By rule, - ( - ) = +
Example 2: Subtract ( - 349)
Solution:
Step 1: Check the signs before each integer. Integers should have one sign in front.
Let us take 250, it is having single sign (+) in front. Now take 349 ,it is having two
signs (- & -) in front.
Step 2: By using Multiplication rule, we make it as single sign
Therefore - (- 349) = + 349
Step 3: Therefore, (-349) =
Step 4: As per Addition rule 1, if the numbers have same sign, add the numbers
and copy bigger number sign
= & Bigger number sign is “+“
By rule, - ( - ) = +
Answer: (- 349) = + 599

8. 275 + 100 = 375 & Bigger number sign is “-“
Example 3 : Subtract (- 275) - (100)
Solution:
Step 1: Check the signs before each integer. Integers should have one sign in front.
Let us take 275, it is having single sign (-) in front. Now take 100 ,it is having single
sign (-) in front.
Step 2: As per Addition rule 1, if the numbers have same sign, add the numbers and
copy bigger number sign
= 375 & Bigger number sign is “-“
Answer: (100) =

9. Try these
1. Subtract (- 222)
2. Subtract (- 345)