Addition of Integers

Integers are whole numbers that can be negative, zero as well as positive in nature. This paper therefore seeks to explore integer addition as one of the most important concepts of mathematics that students must learn since it is the foundation for other more complex concepts. In this article, the author will present a brief introduction of integer addition, the rules to follow, examples and properties, a geometrical representation using a number line, and some common questions related to this topic.

What Are Integers?

Integers can be a positive whole number, a negative whole number or equal to 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 very crucial in mathematics and in real life situations.

Importance of Learning Integer Addition

This is an important aspect because integer addition is a major operation that is widely used in everyday life:

• Learning how to deal with integers is beneficial in building the reasoning process and in solving different problems encountered in everyday life.
• It is very important as it lays down good grounding for more advanced mathematical learning.

Addition of Integers

Integer addition is a process of combining two or more whole numbers together to get the total of the given numbers. This fundamental math operation has three potential outcomes: The data type comes in handy when performing operations such as combining two positives or 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

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

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.

• Example: 5+3=8

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

• Example: −6+(−3)=−9

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

• 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.

• Example: 7+(−5)=2

Properties of Integer Addition

Closure Property: The sum of any two integers is always an integer.

• Example:
• 2+3=5

Commutative Property: The order in which two integers are added does not affect the sum.

• Example:
• a+b=b+a
• 4+(−7)=−7+4

Associative Property: The way in which integers are grouped does not change their sum.

• Example:
• (a+b)+c=a+(b+c)
• (2+3)+4=2+(3+4)

Additive Identity: Adding zero to any integer does not change the value of that integer.

• Example:
• a+0=a
• 6+0=6

Additive Inverse: For every integer, there is another integer such that their sum is zero.

• Example:
• a+(−a)=0
• 5+(−5)=0

Adding Integers on Number Line

Adding integers on a number line involves visually representing the process by starting at the first number and moving right (for positive) or left (for negative) the number of spaces equal to the absolute value of the second number. The point at which you stop represents the sum of the integers.

Step-by-Step Process:

Locate the First Integer: Find the position of the first integer on the number line.

Determine the Direction: If the second integer is positive, move to the right. If it is negative, move to the left.

Move the Number of Spaces: Move the number of spaces equal to the absolute value of the second integer.

Find the Sum: The point where you stop is the sum of the two integers.

Adding Integers with the Same Sign

When adding integers with the same sign, add their absolute values and keep the common sign.

Example:

−4+(−5)=−(4+5)=−9

Adding Integers with Different Signs

When adding integers with different signs, subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the larger absolute value.

Example:

−6+9=9−6=3

Solved Problems - Addition of Integers

Problem: 15 + (-10)

Solution: This means that the total sum of 15 and the subtraction of an amount equal to 10 from the total results in an answer of 5.
You simply need to subtract the absolute value of the negative integer from the positive integer.

Problem: -7 + (-12)

Solution: The result of the sum is -19, if we subtract -12 from -7.
Combine the absolute values and add a sign based on the rule that two negative integers added together gives an answer with a negative sign.

Problem: -3 + 9

Solution: adding and subtracting the corresponding elements in the matrices: -3 + 9 = 6
Here, the absolute value of the negative integer would have to be subtracted from the positive integer.

Problem: -6 + 6

Solution: Although, 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?

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. To get more elaborations and similar types of problems, you may like to look into other articles on GeeksforGeeks.

Addition of Integers - FAQs

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.