1070 LearnersLast updated on June 18th, 2025
Addition And Subtraction of Integers
Addition and subtraction of integers are operations that change the value of the number. Integers consist of whole numbers (0, 1, 2, 3, ….) and negative numbers. In this topic, we are going to talk about adding and subtracting integers and the rules we need to follow.
What are integers?
Adding and subtracting integers involve operations that result in a positive, negative, or zero number. Integers are whole numbers, including positive numbers, negative numbers, and zero. They do not include decimals or fractions.
Positive integers: 1, 2, 3, 4…
Negative integers: -1, -4, -8…
Zero: It is neither positive nor negative.
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Rules for Adding and Subtracting Integers
Adding and subtracting integers follow specific rules that simplify calculations. Addition and subtraction are inverse operations. We can solve problems by using the following rules:
| Integer sign | Operation | Integer Sign after operation is calculated |
| (+a) - (+b) | Subtract | + |
| (+a) - (-b) | Add | + |
| (-a) - (+b) | Add | - |
| (-a) - (-b) | Subtract | - |
Addition and Subtraction of Integers on Number Line
A number line is a horizontal straight line where integers are placed in equal intervals. To add and subtract integers on a number line, we use the following steps:
Addition of integers on a number line:
- If we want to add a positive integer, we move to the right of the number line.
- If we want to add a negative integer, we move to the left of the number line.
Subtraction of integers on a number line:
- If we want to subtract a positive integer, we move to the left of the number line.
- To subtract a negative integer, we move to the right of the number line.
Real-life Applications on Addition and Subtraction of Integers
Addition and subtraction of integers are used in many real-life situations. Here are a few real-world applications where the addition and subtraction of integers are used:
- Banking: In bank accounts, transactions involve deposits where we add money to the account and withdrawals, where money is subtracted out of the account.
- Temperature changes: Meteorologists track temperature changes over time, including a rise (+) in temperature and a decrease (-) in temperature.
- Businesses: Businesses use integers to track profits (+) and losses (-) in financial statements. This is especially useful during accounting and budgeting.
Common Mistakes on Addition and Subtraction of Integers and How to Avoid Them
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Mistake 1
Confusing Addition and Subtraction of Negatives
Students might incorrectly think that -5 - (-3) equals -8 instead of -2. Students must remember that when a negative number is subtracted it is the same as adding the opposite.
Mistake 2
Ignoring the negative sign
When solving problems involving addition and subtraction, students might get confused as to which operation must be used. Always look at the sign before the integer before solving. The final answer will have the same sign as the number with the bigger value.
Mistake 3
Forgetting zero’s rule in addition and subtraction
Students must remember that adding or subtracting zero does not change the number at all. So 15 + 0 = 15 and 15 - 0 = 15, the value will never change.
Mistake 4
Incorrectly applying the commutative property
Students assume that the commutative property applies to both addition and subtraction of integers. But this is incorrect because the commutative property applies only to the addition of integers. In subtraction, if the order is changed, the result will be different. 5 - 2 = 3 and 2 - 5 = -3 gives two different results.
Mistake 5
Misapplying integer rules in word problems
When solving word problems, students may not understand the key terms, such as losing 3 points means - 3 and not +3. Identify increases as positive and decreases as negative before performing any operations.
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Solved Examples on Addition and Subtraction of Integers
Problem 1
What is 7 + (-4)?
3
Explanation
Start at 7 on the number line and move 4 steps left (since -4 is negative). We will land on 3.
Problem 2
Solve -6 + (-8)
-14
Explanation
Both numbers are negative, so add their absolute values: 6 + 8 = 14
Since both numbers are negative, we keep the negative sign. Therefore, the answer is -14.
Problem 3
Calculate (-3) - 5.
-8
Explanation
-3 - 5 is the same as -3 + (-5), which is -8.
Problem 4
Solve -10 + (-2).
-12
Explanation
Both numbers are negative, so we will add their absolute values: 10 + 2 = 12.
We will keep the negative sign since both numbers are negative.
Problem 5
Find 5 - ( -9)
14
Explanation
Subtracting a negative number is similar to adding a positive: 5 - (-9) = 5 + 9.
Perform addition: 5 + 9 = 14.
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FAQs on Addition and Subtraction of Integers
1.How can you add two positive integers?
2.How can a positive integer and a negative integer be added to each other?
3.What is the rule for subtracting integers?
4.What happens when you subtract a positive integer?
5.Does the order matter when we add integers?
6.How can children in Australia use numbers in everyday life to understand Addition And Subtraction of Integers?
7.What are some fun ways kids in Australia can practice Addition And Subtraction of Integers with numbers?
8.What role do numbers and Addition And Subtraction of Integers play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Addition And Subtraction of Integers skills?
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