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Pls,explain commutative and associative property of integers in subtraction

Commutative property under subtraction:

The arithmetic operation subtraction is not commutative for integers. For two integers a and b, a - b ≠ b - a. 

For example,  9 - 5 = 4

whereas 5 - 9 = -4

Hence, 4 ≠ - 4.

Associative property under subtraction:

The subtraction operation is not associative for integers.  For three integers a, b and c,

a - (b - c) ≠ (a - b) - c

For example, 9 - (6 - 3) = 9 - 3 = 6

whereas (9 -6) - 3 = 3 - 3 = 0

Clearly, 6 ≠ 0.

 

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The Commutative Laws (or the Commutative Properties)

The commutative laws state that the order in which you add or multiply two real numbers does not affect the result.

The Commutative Law of Addition:

a + b = b + a

Example:

3 + 5 = 5 + 3 = 8

20 + (–3) = (–3) + 20 = 17

The Commutative Law of Multiplication:

ab = ba

Example:

4 · 5 = 5 · 4 = 20

(–2)(8) = (8)(–2) = –16

The Associative Laws (or the Associative Properties)

The associative laws state the when you add or multiply any three real numbers, the grouping (or association) of the numbers does not affect the result.

The Associative Law of Addition:

(a + b) + c = a + (b + c)

Example:

(2 + 3) + 5 = 5 + 5 = 10

2 + (3 + 5) = 2 + 8 = 10

The Associative Law of Multiplication:

(ab)c = a(bc)

Example:

(5 · 7) · 6 = 35 · 6 = 210

5 · (6 · 7) = 5 · 42 = 210

The Associative Laws (or the Associative Properties)

The associative laws state the when you add or multiply any three real numbers, the grouping (or association) of the numbers does not affect the result.

The Associative Law of Addition:

(a + b) + c = a + (b + c)

Example:

(2 + 3) + 5 = 5 + 5 = 10

2 + (3 + 5) = 2 + 8 = 10

The Associative Law of Multiplication:

(ab)c = a(bc)

Example:

(5 X 7) · 6 = 35 X 6 = 210

5 X (6 X 7) = 5 X 42 = 210

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