1115 LearnersLast updated on June 18th, 2025
Adding Integers
Adding integers refers to a fundamental process of combining two or more integers to find the sum. The nature of the integers influences the result obtained from the addition operation. They can be positive, negative, or a combination of both. In this topic, let us take a closer look at the fundamental arithmetic process of adding integers.
What are integers?
Integers include whole numbers, both positive and negative numbers, as well as zero. They are represented as {..., -3, -2, - 1, 0, 1, 2, 3…}.
Integers do not have fractional or decimal parts. These numbers play a vital role in mathematics and daily life calculations. Numbers that are greater than zero are known as positive integers.
For example, 1, 2, 70, 100, 500, and so on. Numbers that are less than zero are called negative integers, such as -1, -5, -60, and -99. Zero is also an integer, although it is neither positive nor negative.
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What are the Rules for the Addition of Integers?
When we add integers, we must follow certain rules to get the right sum. Integers are whole numbers without fractional parts, including positive, negative numbers, and zero. Here are the basic rules for adding integers:
How to add integers?
- The total of an integer and its opposite number (known as the additive inverse) is always zero (0). For example, 5 + (-5) = 0
10 + (-10) = 0
- The sum of two positive integers is always a positive value. For example, 4 + 4 = 8
- The sum of two negative integers is always a negative number. For instance, (-7) + (-7) = -14
(-8) + (-8) = -16
- When we add zero to any integer, the sum will be the same integer. For example, 11 + 0 = 11
100 + 0 = 100
- When we add a positive number to a negative number, the addition process involves subtracting the smaller absolute value of a smaller number from the larger one. Absolute value shows how far a number is from zero, regardless of its sign. After that, apply the sign of the greater number with the sum.
For instance, +5 - 3 = +2. Here, the absolute values are 5 and 3.
- Subtract the smaller absolute value from the larger absolute value: 5 - 3 = 2
- Add the sign of the largest number, here 5 is the greatest positive number.
Adding integers with the same sign
When we add two integers that have the same sign, then we need to add their absolute values and apply the common sign with the final result.
For example, (-2) + (-9) = - (2 + 9) = -11
3 + 5 = 8
(-2) + (-15) = - (2 + 15) = -17
Adding integers with different signs
When we add integers with different signs, we need to subtract the absolute values and apply the sign of the greatest number with the final answer. For example, To add (-3) and 4:
Absolute values: |-3| = 3, |4| = 4
Find the difference: 4 - 3 = 1
Since 4 is greater and positive, the result is +1
Final Answer: (-3) + 4 = 1
What are the Properties of Addition of Integers?
To understand how the addition of integers works, we must examine its essential properties. Below are the key properties related to the addition of integers.
- Closure property: This property states that the sum of any two integers will be an integer. For example, 4 + 6 = 10.
- Commutative property : The final result of adding two integers will not change, by changing the order of numbers. Mathematically, a + b = b + a.
For instance, 3 + (-6) = -6 + 3 = -3
- Associative property: When we add integers, the way they are organized or grouped does not influence the result. This means, (a +b) + c = a + (b + c).
For instance, (3 + 9) + 6 = 3 + (9 + 6).
- Additive inverse: When we add an integer with its additive inverse, the result is always zero. It means, a + (-a) = 0.
For example, 8 + (-8 ) = 0
Real-life Applications of Adding Integers
In our everyday lives, we use the addition of integers to get accurate mathematical results for real-life problems and mathematical calculations. It is an important skill that everyone should learn in their life. Here are some real-world significance of adding integers:
- Weather forecasters examine the temperature and climate changes using integer addition. For example, a temperature increase can be shown in positive numbers and a temperature decrease can be shown in negative numbers.
- To examine and calculate the profit and loss of a business or company, entrepreneurs can employ integer addition. Profits are represented by positive numbers, while losses can be expressed in negative numbers.
- Teachers use this essential skill of adding integers to evaluate students’ academic performance. For example, if a student scores 80 marks on one test and 50 marks on another, the total score can be calculated as: 80 + 50 = 130
- Sports coaches and teams use positive and negative numbers to record and calculate the scores of players in each round.
Common Mistakes and How to Avoid Them on Adding Integers
In mathematics and daily life calculations, knowledge of the concept of adding integers is essential. However, sometimes students make common mistakes that lead to incorrect integer sums. Here are some common mistakes and their helpful solutions to ensure the accuracy of the calculations.
Mistake 1
Misinterpret the concept of addition and subtraction
Students often make mistakes when they perform calculations related to negative numbers. They may mistakenly subtract the negative numbers when they should be added together.
For example, −2 + (−5) =3 is incorrect. The correct answer is −2 + (−5) = -7.
Mistake 2
Neglecting the negative sign
Kids forget to apply the negative sign in the final result. When we add a positive number to a negative number, first, we need to find the difference between the two numbers' absolute values. After that, apply the sign of the greater number with the sum.
For instance, −4 + 2 = 6 is incorrect. The correct answer is −4 + 2 = -2.
Mistake 3
Placing the wrong sign in the result
Remember to place the correct sign in the final result, otherwise the answers will be inaccurate and misleading.
For example, - 7 + 2 = 9 is incorrect. The correct answer is - 7 + 2 = -5. Here, 7 is greater than 2, then the result should be negative.
Mistake 4
Assuming that the addition of two negative numbers gives a positive result
Sometimes, students mistakenly think that adding two negative numbers will give a positive integer as the result. They think about the multiplication rule (negative ×negative = positive) to addition. However, when two negative numbers are added together, their absolute values are added, then the sum remains negative.
For example, -6 + -4 = -10 is the correct answer.
Mistake 5
Thinking zero can influence the final result
Kids may think that zero influences the final result is a common error. So, keep in mind that zero cannot change the value.
For instance, 9 + 0 = 9.
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Solved Examples of Adding Integers
Problem 1
Find the sum of 7 and 5.
12
Explanation
To find the sum of 7 and 5, we need to add both the numbers:
7 + 5 = 12
Here, both the numbers are positive.
The final answer is 12.
Problem 2
Find the sum of (-7) and (-3).
-10
Explanation
Here, both the numbers are negative. So we can add their absolute values:
7 + 3 = 10
Next, we can keep the negative sign with the sum.
10 = -10
Add (-7) and (-3) to get -10.
Problem 3
Find the sum of 10 and (-5).
5
Explanation
In this case, one number is positive, and the other is negative.
So, we can subtract the absolute values:
10 - 5 = 5
Here, 10 is the largest positive number, so the result will be positive.
The sum of 10 and (-5) is 5.
Problem 4
Add (-8) and 2.
-6
Explanation
Here, -8 is a negative number, and 2 is a positive number.
Hence, we need to subtract the absolute values:
8 - 2 = 6
The largest number is (-8) and it's a negative number. So the result is negative.
6 = -6
The sum of (-8) and 2 is -6.
Problem 5
Find the sum of 10 and 35.
45
Explanation
Here, both the numbers are positive and we can add them normally.
10 + 35 = 45
45 is the sum of 10 and 35.
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FAQs on Adding Integers
1.Define integers.
2.Briefly state the rule for adding two positive integers.
3. Note the rule for adding two negative integers.
4.What happens when you add zero to an integer?
5.How can children in United States use numbers in everyday life to understand Adding Integers?
6.What are some fun ways kids in United States can practice Adding Integers with numbers?
7.What role do numbers and Adding Integers play in helping children in United States develop problem-solving skills?
8.How can families in United States create number-rich environments to improve Adding Integers skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
