# Can subtraction be associative?

**Asked by: Ellis Ebert**

Score: 4.6/5 (67 votes)

Contrary to addition, **subtraction doesn't have the associative property**. If we subtract the first two numbers, 10 minus 5, it gives us 5. ... Changing the way of associating the numbers in subtraction changes the answer. Thus, subtraction doesn't have the associative property.

## Does associative work with subtraction?

Associative property:

Associative law states that the order of grouping the numbers does not matter. This law holds for addition and multiplication but **it doesn't hold for subtraction and division**.

## Is subtraction associative in integers?

Subtraction of integers is **not associative in nature** i.e. x − (y − z) ≠ (x − y) − z.

## Is subtraction of natural numbers associative?

Associative Property – The set of natural numbers is **associative under addition and subtraction** but not under multiplication and division.

**26 related questions found**

### Is there a commutative property of subtraction?

**Commutative property cannot be applied for subtraction and division**, because the changes in the order of the numbers while doing subtraction and division do not produce the same result. For example, 5 - 2 is equal to 3, whereas 3 - 5 is not equal to 3.

### What is the identity property of subtraction?

The identity property of addition is that when a number n is added to zero, the result **is the number itself** i.e. This property holds true for subtraction as well because subtracting 0 from any number equals the number itself. Therefore, 0 is also called a subtractive identity.

### What are the 4 properties of subtraction?

**Properties of subtraction:**

- Subtracting a number from itself.
- Subtracting 0 from a number.
- Order property.
- Subtraction of 1.

### What is associative property of subtraction?

Associative Property

This means that **we cannot group any two whole numbers and subtract them first**. Order of subtraction is an important factor. If 'a', 'b', and 'c' are the three whole numbers then, a − (b − c) ≠ (a − b) − c.

### Why is subtraction not commutative?

Subtraction is not commutative over real numbers since we can't say that **a – b = b – a for all real numbers a and b**. Even though a – b = b – a whenever a and b are the same, that still doesn't make subtraction commutative over the set of all real numbers.

### Does Vector subtraction follow associative law?

**Vector subtraction does not follow associative law** as , one can find ( A → - B → ) and B → - A → individually but in general they are not equal . So associative law does not work in vector subtraction .

### What uses the associative property to make it easier to evaluate?

Use the associative property of multiplication to regroup the factors so that 4 and are next to each other. **Multiplying 4 by first** makes the expression a bit easier to evaluate than multiplying by 27.

### Is distributive property closed under subtraction?

This means that distributive property of multiplication over subtraction holds **true** for all integers.

### Is subtraction commutative example?

**Subtraction is not commutative**. This means that the order of the numbers in the subtraction does matter. For example, 10 – 2 = 8 but 2 – 10 = -8. ... We can switch the order of the 10 and the 2 in the subtraction.

### What are the subtraction properties?

The commutative property and associative property are not applicable to subtraction, but subtraction has a property called **subtractive property of zero**. Subtractive property states that if we subtract zero (0) from any number, the answer or difference will be the non-zero number.

### What are the three types of subtraction?

**But there are actually three different interpretations of subtraction:**

- Taking away.
- Part-whole.
- Comparison.

### What is an example of associative property?

The Associative Property is the **rule that includes grouping of numbers**. For associative property of addition, the rule is "a + (b + c) = (a + b) + c", for example, 2 + (3 + 4) = (2 + 3) + 4 ⇒2+7 = 5+4.

### What is associative property formula?

The associative property formula for rational numbers can be expressed as **(A + B) + C = A + (B + C) or (A × B)** **× C = A × (B × C)**. Here the values of A, B, and C are in form of p/q, where q ≠ 0. The associative property formula is only valid for addition and multiplication.

### What are the subtraction rules?

- Review the following Subtraction Rules and Properties: The Identity Property of Subtraction (also known as the Zero Rule of Subtraction):
- Any number minus zero equals itself. ( 2 – 0 = 2) ...
- one. ( 5 − 1 = 4) ...
- zero. ( 2 – 2 = 0) ...
- the number just before it equals one. ( 3 − 2 = 1)

### How do you explain subtraction?

In math, to subtract means to take away from a group or a number of things. When we subtract, **the number of things in the group reduce or become less**. The minuend, subtrahend and difference are parts of a subtraction problem.

### What is subtraction in math?

Subtraction is **the operation of taking the difference of two numbers** and . Here, is called the minuend, is called the subtrahend, and the symbol between the and is called the minus sign. The expression " " is read " minus ." Subtraction is the inverse of addition, so .

### What are the two properties of subtraction?

- Properties of subtraction.
- Closure property: For any two whole numbers, a and b, if a > b then a – b is a whole number and if a < b then a – b is never a whole number. ...
- Commutative property: For any two whole numbers a and b, a – b ≠ b – a . Hence subtraction of whole number is not commutative. ...
- Associative property:

### What are the 4 types of properties?

There are four basic properties of numbers: **commutative, associative, distributive, and identity**. You should be familiar with each of these.

### Is zero the identity element for subtraction?

The statement, " **0 is the identity element** for subtraction of rational numbers" is true. This is because when 0 is subtracted from any rational number, the answer is the rational number itself. ... Hence, 0 is the identity element of subtraction for rational numbers.