Adding Integers: Definition, Rules & Examples - GeeksforGeeks (2024)

Integers are whole numbers that can be negative, zero as well as positive in nature. Integers stand as the fundamental building blocks for various calculations. From simple arithmetic to complex algorithms, the addition of integers forms the base of numerical operations. It offers a gateway to understanding mathematics’s abstract and practical applications.

In this article, we will learn about integers, addition of integers, rules of integers addition along with some problems based on it.

Table of Content

  • What Are Integers?
  • Addition of Integers
  • How to Add Integers?
  • Rules for Adding Integers
  • Properties of Integer Addition
  • Solved Problems on Addition of Integers
  • Practice Questions on Addition of Integers

What Are Integers?

Integers can be a positive whole number, a negative whole number, or zero. These can be represented as the set {…, -3, -2, – 1, 0, 1, 2, 3…}. Integers are numbers that do not have a fractional or decimal value attached to it. Integers are arithmetic numbers used in calculations, which are crucial in mathematics and real-life situations.

Addition of Integers

Integer addition is a process of combining two or more integers together to get the total of the given numbers. This fundamental math operation has three potential outcomes:

  • Addition of two positives
  • Addition of two negatives or
  • Adding a positive and negative number.

How to Add Integers?

In order to add integers, it is necessary to pay attention to the sign placed before them. If the signs are alike, to the answer add absolute values and give the sum that has the sign that is common to both numbers.

If the signs are different, the result of subtraction should be the absolute value of the quantity which is greater minus the absolute value of the quantity which is smaller. The difference is that the sign is given to the integer having the biggest absolute value.

Rules for Adding Integers

Below are the rules of integer addition:

Condition

Rule

Same Sign

Add the absolute values and keep the common sign.

Different Signs

Subtract the smaller absolute value from the larger one and take the sign of the larger absolute value.

Adding Positive Integers

When combining two positive whole numbers, add the values.

Adding Negative Integers

When combining two negative whole numbers, add the absolute values and give the result a negative sign.

Demonstration of Rules

Below is the demonstration of the rules discussed above:

Adding Positive Integers: When combining two positive whole numbers, you add up the value of each one. The sum of two positive integers is always positive.

For Example: 5 + 3 = 8

Here 5 and 3 both are positive and hence there sum i.e. 8 is also positive.

Adding Negative Integers: When adding two negative integers, add their absolute values and give the result a negative sign.

For Example: −6 + (−3) = −9

Here -6 and -3 both are negative and hence there sum i.e. -9 is also negative.

Adding Integers with the Same Sign: When both integers have the same sign, add their absolute values and keep the common sign.

For Example: −4 + (−5) = −9

Adding Integers with Different Signs: When the integers have different signs, subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the larger absolute value.

For Example: 7 + (−5) = 2

Here 7 > 5 hence sub 5 from 7 that will be 2, and the sign of 7 will be taken. Hence the answer turned to +2.

Properties of Integer Addition

Integer addition has several important properties that are fundamental to understanding how integers behave under addition. The following are the properties of integer addition:

Closure Property: It states that the sum of any two integers is always an integer.

For Example: 2 + 3 = 5

Commutative Property: It states that the order in which two integers are added does not affect the sum. i.e. a + b = b + a

For Example: 4 + (−7) = −7 + 4 = -3

Associative Property: It states that the way in which integers are grouped does not change their sum. i.e. (a+b) + c = a + (b+c)

For Example: (2+3) + 4 = 2 + (3+4)

Additive Identity: Adding zero to any integer does not change the value of that integer, i.e. a+0=a

For Example: 6 + 0 = 6

Additive Inverse: For every integer, there is another integer such that their sum is zero, i.e. a + (−a) = 0

For Example: 5 + (−5) = 0

Solved Problems on Addition of Integers

Problem 1: Solve 15 + (-10)

Solution:

15 + (-10)

Here, the integers have different signs, subtract the smaller absolute value i.e 10 from the larger absolute value i.e. 15 and take the sign of the integer with the larger absolute value.

Hence the result is +5

Problem2 : Solve -7 + (-12)

Solution:

Here both the integers are negative, When adding two negative integers, add their absolute values and give the result a negative sign.

The result of the sum is -19.

Problem: Solve: -6 + 6

Solution:

The result of operation 6 – 6 equals to 0
Two integers that are opposite each other and have equal absolute values when added, the result will always be zero.

Practice Questions on Addition of Integers

Q1. Compute the sum of -8 and 3.

Q2. Add -15 and -7.

Q3. Find the sum of 4 and 18.

Q4. Calculate -21 plus 19.

Q5. What is the result of adding 14 and -16?

Also Read,

  • Properties of Integers
  • Operations of Integers
  • Whole Numbers

Conclusion

Understanding of the process of adding integers is critical for the further learning of math and applying these skills in real life. Therefore, through understanding of the guidelines, attributes and applications of adding integers, learners will be in a good position to develop a robust mathematics foundation.

FAQs on Addition of Integers

What is the sum of -5 and 8?

−5+8=3

How do you solve two negative numbers when they are together?

Sum the absolute values of the numbers, but add a negative sign to this sum. Example: −4+(−7)=−11

What is the additive identity?

Zero is the additive identity because adding zero to any integer does not change its value. Example: 6+0=6

Can the sum of two negative integers be positive?

No, the sum of two negative integers will always be negative because the addition of any two negative integers will only produce another negative integer.

How can I use a number line to add integers?

Start from the first number on the number line, move right for positive integers, and left for negative integers.



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