Rules to Subtract Integers

Integers are positive and negative number including zero and does not include the fractional part. We will discuss about the rules for subtracting of integers. There are certain rules which will help us in better understanding of subtraction of integers. This topic will discuss how integers are subtracted when:

  • One positive integer is subtracted from another positive integer.
  • One negative integer is subtracted from another negative integer.
  • One positive integer is subtracted from another negative integer.
  • One negative integer is subtracted from another positive integer.

Rules: When two integers’ p and q are subtracted, then for subtracting q from p the sign of q is changed and after that it is added it to p.

Note: For calculation, and for carrying out subtraction:

  • (-) × (+) = (-)
  • (-) × (-) = (+)
  • (+) × (+) = (+)
  • (+) × (-) = (-)

When two signs are written side by side then it is considered that the two signs are multiplied.


Few examples are solved here using the rules of subtraction of integers mentioned above:

1. Subtract 10 from 5

5 – (+10)

Þ 5 – 10 = - 5

Here according to the rule negative sign and positive sign [i.e. (-) × (+) = (-)] makes negative sign. That is why – (+10) will be – 10. So it will be 5 – 10 = -5. Actually the absolute values are subtracted and in the result the value with a higher absolute value is considered.


2. Subtract -11 from 16

16 – (-11)

Þ 16 + 11 = 27

Here according to the rule negative sign and negative sign [i.e. (-) × (-) = (+)] makes positive sign. That is why – (-11) = +11. So it will be 16 + 11 = 27. Here both 16 and 11 is added to get 27.


3. Subtract 9 from -6

= - 6 – (+9)

= - 6 – 9

= -15

Here according to the rule negative sign and positive sign [i.e. (-) × (+) = (-)] makes negative sign. That is why – (+9) will be -9. So it will be - 6 – 9 = -15. Actually the absolute values are added and the result will have negative sign as both the numbers are negative.


4. Subtract -11 from -5

= -5 – (-11)

= -5 +11

= 6

Here according to the rule negative sign and negative sign [i.e. (-) × (-) = (+)] makes positive sign. Therefore – (- 11) = 11. So it will be -5 + 11 = 6. Actually the absolute values are subtracted and in the result the value with a higher absolute value is considered.


Rules to Subtract Integers


5. Subtract -5 from 16

 = 16 – (- 5)

= 16 + 5

= 21

Here according to the rule negative sign and negative sign [i.e. (-) × (-) = (+)] makes positive sign. Therefore – (-5)= +5. So it will be 16 +5 = 21. Here both 16 and 5 is added to get 21.








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