Algebraic Field Properties?

Question

Does anyone know the algebraic field properties for the following?

6x+9x=15x

(1/7)(1/5)=(1/35)

(5)(1/5)=1

If a=b, and b=7, then a=7

Answer 1

The field properties are the properties of real numbers.

(5)(1/5) = 1 is definitely the inverse property of multiplication.
If a = b and b = 7, then a = 7 is definitely the transitive property of equality.

The others are not as definite, and it depends a bit on how your book/teacher interprets and names things.

Most likely the first is the distributive property, because it's equivalent to 6x + 9x = (6+9)x. (However, substitution is also being used here.)

(1/7)(1/5) = (1/35) is most likely substitution (or replacement, which is a different name for the same property). That's not really a standard "field property", but it is normally learned together with them.