Integers are whole numbers (no decimals) that can be either positive or negative (i.e, \(+2, 10, +52, 1\) ). Positive and negative integers appear in our lives everyday: the temperature, depositing or withdrawing money at the bank, walking up a hill or down a hill. You can think of numbers on a number line where \(0\) is in the middle, positive numbers are to the right and negative numbers are to the left.
We can add, subtract, multiply and divide positive and negative integers. There are a few rules we will need to follow.
When adding and subtracting integers, think about moving on the number line. Moving in the positive direction means moving to the right. Moving in the negative direction means moving to the left.
We can also simplify expressions that have multiple signs (\(+\) or \(\)) beside each other. If the signs are the same, replace it with a \(+\) sign. If the signs are different, replace it with a \(\) sign. You can also switch the order of a \(+\) and \(\) sign.
Operation  Rule  General Example  Example 
Addition  When you add integers with the same sign, you add the numbers and keep the sign.  \((+) + (+) = (+)\)  \( (+5) + (+7) = +12\) 
\(() + () = ()\)  \( (3) + (2) = 5 \)  
When you add integers with different signs, you subtract the numbers and keep the sign of the bigger number.  \((+) + \large{()} = ()\)  \( (+5) + (7) \) \((75) = 2\) 

\(\large{(+)} + \normalsize{()} = \large{(+)}\)  \( (+15) + (10)\) \( +(1510) = +5\) 

Subtraction  When you subtract integers with the same signs, switch the sign of the second integer and turn the question into addition. Then use the rules for addition.  \((+)  (+) = (+) + ()\)  \( (+5)  (+7) \) \(= (+5) + (7) = 2\) 
\(()  () = () + (+) \)  \( (15)  (10)\) \( =(15) + (+10) = 5\) 

When you subtract integers with different signs, switch the sign of the second integer and turn the question into addition. Then use the rules for addition.  \(()  (+) = () + ()\)  \( (5)  (+7)\) \( = (5) + (7) = 12\) 

\((+)  () = (+) + (+) \)  \( (+15)  (10)\) \( = (+15) + (+10) = +25\) 

Multiplication  When you multiply integers with the same sign, the answer is positive.  \( (+) * (+) = (+) \)  \( (+5) * (+2) = (+10) \) 
\( () * () = (+) \)  \( (5) * (2) = (+10) \)  
When you multiply integers with different signs, the answer is negative.  \( () * (+) = () \)  \( (5) * (+2) = (10) \)  
\( (+) * () = () \)  \( (+5) * (2) = (10) \)  
Division  When you divide integers with the same sign, the answer is positive.  \( (+) / (+) = (+) \)  \( (+10) / (+2) = (+5) \) 
\( () / () = (+) \)  \( (10) / (2) = (+5) \)  
When you divide integers with different signs, the answer is negative.  \( () / (+) = () \)  \( (10) / (+2) = (5) \)  
\( (+) / () = () \)  \( (+10) / (2) = (5) \) 
\( 12  (3)\)
\( 4*(2) \)
While we are talking about operations with integers, it is helpful to remind you about order of operations. When you have an expression like \( (4  (3)) * 2\) there is an order that we need to follow.
Two common acrynoms are helpful for remembering the order of operations BEDMAS and PEMDAS:


These serve as reminders for which part of the expression we should do first. One important feature is that multiplication/division and addition/subtraction happen at the same time, just in the order they occur from left to right.