Properties of Subtraction
2026-02-28 13:09 Diff

207 Learners

Last updated on August 13, 2025

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.

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Problem 1

Using subtraction: 15 - 9 = 6. This operation shows taking away 9 from 15.

Okay, lets begin

What is the result of (20 - 5) - 3 compared to 20 - (5 - 3)?

Explanation

(20 - 5) - 3 = 12, whereas 20 - (5 - 3) = 18.

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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.

Okay, lets begin

What is the result of subtracting zero from 13?

Explanation

The result is 13.

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Problem 3

Subtracting zero from any number leaves it unchanged, so 13 - 0 = 13.

Okay, lets begin

If 11 - 7 = 4, what should be added to 4 to get back to 11?

Explanation

Add 7 to 4 to get 11.

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Problem 4

Subtraction is the inverse of addition. If 11 - 7 = 4, then adding 7 to 4 gives 11: 4 + 7 = 11.

Okay, lets begin

If you have 25 apples and you give away 8, how many apples do you have left?

Explanation

You have 17 apples left.

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No, subtraction is not commutative. Changing the order of numbers changes the result.

1.What is the identity element in subtraction?

The identity element in subtraction is zero. Subtracting zero from any number leaves it unchanged.

2.Is subtraction associative?

No, subtraction is not associative. Changing the grouping of numbers changes the result.

3.How is subtraction related to addition?

Subtraction is the inverse operation of addition. If a - b = c, then c + b = a.

4.How can subtraction be understood in practical terms?

Subtraction can be understood as "taking away" or removing quantities, illustrating the concept of difference.

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.

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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.