109 LearnersLast updated on 13 August 2025
Properties of Subtraction
Subtraction is a fundamental arithmetic operation with unique properties that simplify mathematical problem-solving. Understanding these properties helps students analyze and solve problems efficiently. The properties of subtraction are centered around the concepts of taking away, difference, and the inverse relationship with addition. These properties allow students to explore concepts such as inverse operations, zero as an identity, and the non-commutative nature of subtraction. Let us learn more about the properties of subtraction.
What are the Properties of Subtraction?
The properties of subtraction are straightforward and help students grasp this essential arithmetic operation. These properties stem from the foundational principles of mathematics. There are several properties of subtraction, and some of them are mentioned below: Property 1: Non-Commutative Subtraction is not commutative, meaning that changing the order of the numbers changes the result. For example, 5 - 3 is not equal to 3 - 5. Property 2: Non-Associative Subtraction is not associative, meaning the grouping of numbers affects the result. For example, (10 - 5) - 2 is not the same as 10 - (5 - 2). Property 3: Identity Element When you subtract zero from any number, the number remains unchanged. For example, 7 - 0 = 7. Property 4: Inverse Operation Subtraction is the inverse operation of addition. If a - b = c, then c + b = a. Property 5: Subtraction as "Taking Away" Subtraction can be understood as taking away or removing quantities from a set, illustrating the concept of difference.
Tips and Tricks for Properties of Subtraction
Students often confuse and make mistakes while learning the properties of subtraction. To avoid such confusion, we can follow these tips and tricks: Non-Commutative Nature: Students should remember that subtraction is not commutative, and changing the order of the numbers will change the result. Non-Associative Nature: Students should remember that subtraction is not associative, and grouping different parts of an equation will yield different results. Identity Element: Students should remember that subtracting zero from any number leaves the number unchanged. Inverse Relationship with Addition: Students should practice using subtraction as the inverse of addition to verify calculations.
Assuming Subtraction is Commutative
Students should remember that subtraction is not commutative. For example, 6 - 2 is not equal to 2 - 6.
Mistake 1
Misapplying Associative Property
Students should know that subtraction is not associative. For example, (12 - 4) - 2 is not the same as 12 - (4 - 2).
Mistake 2
Ignoring the Identity Element
Students should remember that subtracting zero from any number leaves it unchanged. For example, 9 - 0 = 9.
Mistake 3
Forgetting the Inverse Relationship
Students should remember that subtraction is the inverse of addition. If 8 - 3 = 5, then 5 + 3 = 8.
Mistake 4
Overlooking the Concept of "Taking Away"
Students must remember that subtraction often represents the idea of taking away or decreasing quantities, which is fundamental to understanding the operation.
Mistake 5
Solved Examples on the Properties of Subtraction
If you subtract 9 from 15, what will be the result?
The result is 6.
Problem 1
Using subtraction: 15 - 9 = 6. This operation shows taking away 9 from 15.
What is the result of (20 - 5) - 3 compared to 20 - (5 - 3)?
Explanation
(20 - 5) - 3 = 12, whereas 20 - (5 - 3) = 18.
Problem 2
Subtraction is not associative, so grouping affects the result. Calculating separately: (20 - 5) - 3 = 15 - 3 = 12, and 20 - (5 - 3) = 20 - 2 = 18.
What is the result of subtracting zero from 13?
Explanation
The result is 13.
Problem 3
Subtracting zero from any number leaves it unchanged, so 13 - 0 = 13.
If 11 - 7 = 4, what should be added to 4 to get back to 11?
Explanation
Add 7 to 4 to get 11.
Problem 4
Subtraction is the inverse of addition. If 11 - 7 = 4, then adding 7 to 4 gives 11: 4 + 7 = 11.
If you have 25 apples and you give away 8, how many apples do you have left?
Explanation
You have 17 apples left.
No, subtraction is not commutative. Changing the order of numbers changes the result.
1.What is the identity element in subtraction?
2.Is subtraction associative?
3.How is subtraction related to addition?
4.How can subtraction be understood in practical terms?
5.How can children in Australia use numbers in everyday life to understand Properties of Subtraction?
6.What are some fun ways kids in Australia can practice Properties of Subtraction with numbers?
7.What role do numbers and Properties of Subtraction play in helping children in Australia develop problem-solving skills?
8.How can families in Australia create number-rich environments to improve Properties of Subtraction skills?
Common Mistakes and How to Avoid Them in Properties of Subtraction
Students often get confused when understanding the properties of subtraction and tend to make mistakes while solving related problems. Here are some common mistakes students tend to make and solutions to avoid them.
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.
