what properties were used to write the numeric statement (18 - 5) + (432 x 15) = (15 x 432) + (18 - 5)

The properties that have been used are the;

commutative property of addition

commutative property of multiplication

Step-by-step explanation:

The commutative property of addition can be stated algebraically as follows;

a + b = b + a

where a and b are any real numbers

On the other hand, the commutative property of multiplication can be stated algebraically as follows;

a * b = b * a

where a and b are any real numbers

If we let 18 - 5 = a, 432 = m and 15 = n, then we have;

a + (m * n)

Using the commutative property of addition, the expression can be written as;

(m * n) + a

Using the commutative property of multiplication, the term in brackets can be written as;

(m * n) = (n * m)

Combining the two properties we find that;

a + (m * n) = (m * n) + a = (n * m) + a

Therefore, (18 - 5) + (432 x 15) = (15 x 432) + (18 - 5)