Question: List down the rules for adding, subtracting, multiplying and dividing positive and negative numbers.

The four basic arithmetic operations associated with integers are:

• Addition of Integers
• Subtraction of Integer
• Multiplication of Integers
• Division of Integers

Answer: There are some rules for adding, subtracting, multiplying, and dividing positive and negative numbers.

Before we start learning these methods of integer operations, we need to remember a few things. If there is no sign in front of a number, it means that the number is positive.

Explanation:

The following content shows the rules for adding, subtracting, multiplying, and dividing positive and negative numbers.

Adding Integers Rule:

Case 1: Signs are the same

If the signs are the same, add and keep the same sign.

• (+) + (+) = Add the numbers and the answer is positive

           Example : 2 + 5 = 7

• (‐) + (‐) = Add the numbers and the answer is negative

           Example : (-5) + (-4) = -9

Case 2: Signs are different

If the signs are different, subtract the numbers and use the sign of the larger number.

• (+) + (‐) = Subtract the numbers and take the sign of the bigger number.

           Example: 7 + (-3) = 4

• (‐) + (+) = Subtract the numbers and take the sign of the bigger number.

          Example: (-9) + 6 = -3

Subtracting Integers Rule:

To subtract a number from another number, the sign of the number (which is to be subtracted) should be changed and then this number with the changed sign should be added to the first number.

• (+) - (+) = Change the sign of the number to be subtracted and add them up. The result takes the sign of the greater number.

            Example: (+6) – (+2)

                           = (+6) + (-2) = 6 - 2 = 4

• (-) - (-) = Change the sign of the number to be subtracted and add them up.The result takes the sign of the greater number.

           Example: (-9) – (-6)

                         = (-9) + (+6) = -9 + 6 = -3

• (+) - (-) = Change the sign of the number to be subtracted and add them up.

           Example: (+5) – (-3)

                         = (+5) +(+3) = 5 + 3 = 8

• (-) - (+) =  Change the sign of the number to be subtracted and add them up. Result is always negative

           Example: (-7) – (+2)

                         = (-7) + (-2) = -7 - 2 = -9

Multiplying and Dividing Integers Rule:

Case 1: Signs are same

If the signs are the same, the answer is always positive.

• (+) × (+) = + 

           Example: 5 × 4 = 20

• (+) ÷ (+) = +

           Example: 16 ÷ 4 = 4

• (‐) × (‐) = + 

           Example: (-7) × (-9) = 63

• (‐) ÷ (‐) = +

            Example: (-20) ÷ (-2) = 10

Case 2: Signs are different

If the signs are different, the answer is always negative.

• (+) × (‐) = ‐

           Example: 6 × (-10) = -60

• (+) ÷ (‐) = ‐

           Example: 30 ÷ (-15) = -2

• (‐) × (+) = ‐

           Example: -3 × 11 = 33

• (‐) ÷ (+) = ‐

           Example: -25 ÷ 5  = -5

Thus, these are the rules to add, subtract, multiply and divide positive and negative numbers.