Question

It is said that 'Decimal numbers and whole numbers have the same properties
of addition Verify the commutative and associative properties for decimal
numbers​

Answer 1

Explanation:

the answer is yes ......

Answer 2

Commutative Property

Simply put, the commutative property states that the factors in an equation can be rearranged freely without affecting the outcome of the equation. The commutative property, therefore, concerns itself with the ordering of operations, including the addition and multiplication of real numbers, integers, and rational numbers.

For example, the numbers 2, 3, and 5 can be added together in any order without affecting the final result:

2 + 3 + 5 = 10

3 + 2 + 5 = 10

5 + 3 + 2 = 10

The numbers can likewise be multiplied in any order without affecting the final result:

2 x 3 x 5 = 30

3 x 2 x 5 = 30

5 x 3 x 2 = 30

Subtraction and division, however, are not operations that can be commutative because the order of operations is important. The three numbers above cannot, for example, be subtracted in any order without affecting the final value:

2 - 3 - 5 = -6

3 - 5 - 2 = -4

5 - 3 - 2 = 0

As a result, the commutative property can be expressed through the equations a + b = b + a and a x b = b x a. No matter the order of the values in these equations, the results will always be the same.

Associative Property

The associative property states that the grouping of factors in an operation can be changed without affecting the outcome of the equation. This can be expressed through the equation a + (b + c) = (a + b) + c. No matter which pair of values in the equation is added first, the result will be the same.

For example, take the equation 2 + 3 + 5. No matter how the values are grouped, the result of the equation will be 10:

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

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

As with the commutative property, examples of operations that are associative include the addition and multiplication of real numbers, integers, and rational numbers. However, unlike the commutative property, the associative property can also apply to matrix multiplication and function composition.

Like commutative property equations, associative property equations cannot contain the subtraction of real numbers. Take, for example, the arithmetic problem (6 – 3) – 2 = 3 – 2 = 1; if we change the grouping of the parentheses, we have 6 – (3 – 2) = 6 – 1 = 5, which changes the final result of the equation.