How to Apply Integers Addition and Subtraction Rules?

Using the rules of addition and subtraction, two integers can be easily added or subtracted. In this step-by-step guide, you will learn these rules.

How to Apply Integers Addition and Subtraction Rules?

Addition and subtraction of integers are two operations we perform on integers to increase or decrease their values. Every number shown on a number line that has no fractional part is an integer.

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Step by step guide to applying integers addition and subtraction rules

Rules for adding integers

Certain rules must be followed to add two or more integers. Integers are complete numbers that do not have fractional parts. This includes positive, zero, and negative integers. The rules for adding integers are as follows:

  • The sum of an integer and its inverse is \(0\).
  • Adding two positive integers always gives in a positive value that is greater than both the integers.
  • Adding two negative integers always gives a negative number smaller than the given numbers.
  • The addition of a positive number to a negative number is done by finding the difference between the absolute values of both numbers. Then, the sign with the greater number gets attached to the sum.
  • Adding integers with 0 results in the same number.

The rules of the addition of integers can be understood with the help of the table below.

Rules for subtracting integers

The rules for subtracting integers are given below:

  • If we subtract \(0\) from any integer, the answer will be the integer itself.
  • If we subtract any integer from 0, we will find the opposite of the integer.
  • Subtraction of integers is done by changing the sign of the subtrahend. After this step, if both numbers are from the same symbol, we add the absolute values and attach the common symbol to it. If both numbers have different symbols, we find the difference between the absolute numbers and put the sign of the bigger number in the result.

The table below shows the rules for subtracting an integer with an example.

Applying Integers Addition and Subtraction Rules – Example 1:

Using the rules for the addition of integers, find which number should be subtracted from \(15\) to get \(-9\) as the answer?

Solution: 

Suppose \(x\) must be subtracted from \(15\) to \(-9\). Therefore, we can form an equation in terms of \(x\).

\(15-x= -9\)

\(-x = -9 -15\)

\(-x=-24\)

\(x = 24\)

Therefore, \(24\) has to be subtracted from \(15\) to get \(-9\).

Applying Integers Addition and Subtraction Rules – Example 2:

Subtract \(-8\) from \(-13\) using the rules of subtracting integers.

Solution: 

Here we need to subtract two integers with the same sign, \(-13\) and \(-8\).

\(-13- (-8) = -13 + 8\)

\(=-5\)

Exercises for Applying Integers Addition and Subtraction Rules

Perform the following calculations using the addition and subtraction rules.

  1. \(\color{blue}{(-5)+9}\)
  2. \(\color{blue}{-11-19}\)
  3. \(\color{blue}{8 – 10 +(-4) + 7}\)
  4. \(\color{blue}{(-16) + (-24)}\)
  5. \(\color{blue}{(-3)-(-5)-(-12)}\)
This image has an empty alt attribute; its file name is answers.png
  1. \(\color{blue}{4}\)
  2. \(\color{blue}{-30}\)
  3. \(\color{blue}{1}\)
  4. \(\color{blue}{-40}\)
  5. \(\color{blue}{14}\)

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