What Are the Properties of Subtraction With Rules and Examples
According to the algebraic concept known as the "subtraction property of equality," if a value is subtracted from two equal quantities, the resulting differences are also equal.
The subtraction property of equality states that in order to maintain equality if we take a number away from one side of equality, we must also take that same amount away from the other side.
Comparable to the equality's addition property is this property. The properties of equality range from the addition property to the division property to the reflexive property to the multiplication property, among others. By applying the identical mathematical operation of subtraction to both sides of an equality, the subtraction property of equality seeks to balance an equation.
Let's look at an illustration to comprehend this better. There are two bags with ten balls each. Now, if we remove three balls from bag 1, we must remove three from bag 2 to maintain the same number of balls in bags 1 and 2. Thus, after releasing three balls from each bag, there are seven balls left in each bag.
Subtraction of 5-Digit Number
Properties of Whole-Number Subtraction
Property 1:
If two whole numbers a and b are such that A > B or A = B, then A - B is also a whole number. If A < B, then it is impossible to subtract B from A in whole numbers.
For instance,
10 - 5 = 5
23 - 12 = 11
100 - 99 = 1
Property 2: Commutative Property of Subtraction
Whole numbers cannot be subtracted cumulatively, hence even if a and b are both whole numbers, a - b does not always equal (B - A).
Verification:
We are aware that 9 – 5 = 4, however, 5 – 9 is illogical. Additionally, 125 - 75 = 50, but 75 - 125 is impractical. In other words, if A > B, then A - B is a whole number but B - A is not feasible, and if B > A, then B - A is a whole number but A - B is not possible for two whole numbers A and B. This is the Commutative property of subtraction.
Therefore, (A -B) is generally not equal to (B - A).
Property 3:
A - 0 equals A if a is any whole number other than zero, but 0 - A is not defined.
Verification:
Although 0 - 15 is not feasible, we know that 15 - 0 equals 15.
Property 4: Associative Property of Subtraction
Whole number subtraction is not associative. In other words, if A, B, and C are three whole numbers, A - (B - C) is generally not equivalent to (A - B) - C. This is the Associative Property of Subtraction.
Verification:
Associative Property of Subtraction Example
10 - (9 - 3) = 10 - 6 = 4,
thus, (10 - 9) - 3 = 1 - 3 = - 2
Now because of that 10 - (9 - 3) (10 - 9) - 3.
Zero Property of Subtraction
When a number is subtracted from zero, the result is the original number.
For instance,
(i) 5645 - 0 = 5645;
(ii) 987 - 0 = 987
Properties of a Number Subtracted from Itself
The difference is zero when a number is subtracted from itself, according to the properties of subtraction.
For instance,
323 - 323 = 0
12 - 12 =0
Properties of Subtraction Worksheet
Children can practise from properties of subtraction worksheets.
Properties of Subtraction Worksheet
Summary
A mathematical process called subtraction involves taking a portion of one value and subtracting it from another. You subtract two numbers when you do subtraction. The minuend is the initial digit in a subtraction equation. This is the figure from which we deduct. The subtraction is the name of the second number. We take away this from the minute. When we subtract, the result is the difference.
FAQs on Properties of Subtraction in Mathematics
1. What are the properties of subtraction in maths?
The properties of subtraction describe how numbers behave when one number is subtracted from another, including the non-commutative, non-associative, and identity property. These properties help in understanding subtraction rules in arithmetic.
- Non-commutative property: Changing the order changes the result.
- Non-associative property: Grouping affects the result.
- Identity property: Subtracting 0 keeps the number the same.
2. Is subtraction commutative?
No, subtraction is not commutative because changing the order of numbers changes the result. In subtraction, a − b ≠ b − a in most cases.
- Example: 8 − 3 = 5
- But 3 − 8 = −5
3. Is subtraction associative?
No, subtraction is not associative because the way numbers are grouped changes the result. In general, (a − b) − c ≠ a − (b − c).
- (10 − 5) − 2 = 5 − 2 = 3
- 10 − (5 − 2) = 10 − 3 = 7
4. What is the identity property of subtraction?
The identity property of subtraction states that subtracting zero from any number gives the same number, written as a − 0 = a. Zero is called the identity element for subtraction.
- Example: 15 − 0 = 15
- Example: −7 − 0 = −7
5. What is the closure property of subtraction?
The closure property of subtraction depends on the number set being used. Whole numbers are not closed under subtraction, but integers are closed under subtraction.
- Whole numbers: 3 − 5 = −2 (not a whole number)
- Integers: 3 − 5 = −2 (still an integer)
6. What is the formula for subtraction?
The basic subtraction formula is a − b = c, where a is the minuend, b is the subtrahend, and c is the difference. It represents taking away one number from another.
- Minuend: Number being subtracted from
- Subtrahend: Number being subtracted
- Difference: Final answer
7. What is the difference between subtraction and addition properties?
The key difference is that addition is commutative and associative, while subtraction is neither commutative nor associative. This means order and grouping matter in subtraction but not in addition.
- Addition: 4 + 6 = 6 + 4 = 10
- Subtraction: 6 − 4 = 2, but 4 − 6 = −2
8. Can you give an example of the non-associative property of subtraction?
An example of the non-associative property of subtraction is when changing brackets changes the result. Subtraction does not give the same answer when regrouped.
- (20 − 8) − 4 = 12 − 4 = 8
- 20 − (8 − 4) = 20 − 4 = 16
9. Does subtracting a number from itself follow any property?
Yes, subtracting a number from itself always gives 0, written as a − a = 0. This is related to the additive inverse concept in arithmetic.
- Example: 9 − 9 = 0
- Example: −5 − (−5) = 0
10. What are common mistakes when using properties of subtraction?
The most common mistake is assuming subtraction follows the commutative or associative property like addition. This leads to incorrect answers.
- Wrong: Assuming 7 − 2 = 2 − 7
- Wrong: Treating (a − b) − c as a − (b − c)
- Forgetting that whole numbers are not closed under subtraction
