Addition of Integers

Addition of integers is a fundamental arithmetic operation essential for various mathematical tasks and real-life applications. Addition of integers forms the basis for solving equations, managing finances, and analyzing data.

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.

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 sum of the given numbers. This fundamental math operation has three potential cases:

• Addition of two positive integers.
• Addition of two negative integers.
• Adding a positive and negative integer.

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 addition should be the absolute value of the quantity which is greater minus the absolute value of the quantity which is smaller. The sign given to result is the sign of the integer having the biggest absolute value.

Rules for Addition of Integers

Below are the rules for addition of integers:

Demonstration of Rules for Integers Addition

Below is the demonstration of the rules discussed above:

Addition of 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.

Addition of 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.

Addition of 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

Addition of 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 Addition of Integers

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

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 Integers Addition

Problem 1: Solve 15 + (-10)

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

Problem 2 : Solve -7 + (-12)

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 3. Solve: -6 + 6

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 Integers Addition

Question 1. Compute the sum of -8 and 3.

Question 2. Add -15 and -7.

Question 3. Find the sum of 4 and 18.

Question 4. Calculate -21 plus 19.

Question 5. What is the result of adding 14 and -16?

Also Read,

• Properties of Integers
• Operations of Integers
• Whole Numbers

Conclusion

Addition of integers is a fundamental skill in arithmetic that forms the basis for more advanced mathematical concepts. Understanding of the process of adding integers is critical for the further learning of math and applying these skills in real life. Therefore, By understanding how to add positive and negative integers, understanding of the strategies , guidelines, attributes and applications of adding integers, learners will be in a good position to develop a robust mathematics foundation. This knowledge is also important for everyday calculations, algebraic operations, and real-world applications.