Mathematics - Is there preference over the properties of equality?

Question

2x= 4

Multiplication Property of Equality (Multiply both sides by 1/2)

Or Division Property of Equality (Divide both sides by 2)?

Is there a "standard" that dictates that one property is favored over another?

Answer 1

Divide both sides by two.

x=2

Answer 2

I took Geometry Honors where we spent a lot of times learning about Proofs. This is a use of Division Property of Equality. If you want to know how this is explained. I have a large list of the proofs that is worth reading for future mathematics.

My proof that explains this is the proof that any number divisible by 2 is an even. This may not sound like it answers it, but read it, it will. It will also explain addition to back up the multiplication.

1+1=2 (odd+odd=even), 1+3=4 (same), 3+3=6 (same) 2+2=4 (even+even=even), 2+4=6 (same), 1+2=3 (odd+even=odd), 3+2=5 (same)

This shows that any number plus it self equals even. Also that even + odd will always be odd.

Standard way to describe an even is the equation: 2x. Odds are 2x+1 (even + odd). To determine if a number is even is X/2 (Number divided by 2). If the number remains with a .5 or 1/2 in the answer of that, it is an odd, because adding 1 to the equation will give you a whole answer.

2x=4   -   2x is the equal to the even equation. 4 is divisible by 2 with a whole answer. Seeing that "x" is a universal number. 4/2 = x, stating that. This is a use of the Division Property of equality.

Answer 3

They're exactly the same thing. Think of it using fractions. Both are identical.

When you get into more complicated things there will be preferences. Evaluating integrals for instance... some methods get really messy, others stay clean. But it sounds like that's a maybe a couple years off still =]