The Quality of Equality Examples

Identify the property exemplified here. Turkey Sandwich = Turkey Sandwich.

A turkey sandwich is a turkey sandwich no matter how you look at it. Just like contortionists. They can be quite flexible (or reflexible), but they're still the same thing. This is an example of the reflexive property.

We're given that A = B and C = D. As a result, we state that A – C = B – D. This equation is an example of which property or properties?

Well let's take a look-see. If we take A = B and we subtract the same number from it, that's the subtraction property. That gives us A – C = B – C, right? The problem is that we're subtracting C from A and D from B. For that property to be true, we need C to be the same as D. Luckily, we're told that right off the bat. That way, we can make use of the substitution property and replace a C with a D. That'll give us A – C = B – D.

If A = X, B = Y, and C = Z, then can we say that A(B + C) = ZY + XZ?

Nope. If we look carefully at the left side of the equation and apply the substitution property, we get X(Y + Z). Then, the distributive property gives us XY + XZ. We can't be sure that ZY is the same as XY, so that isn't right.

If A + B = C, then is it possible to claim that X(A + B) = CX? Which properties allow us or forbid us from doing so?

It's not only possible. It's possimpible. First off, the multiplication property allows us to multiply both sides of an equation by the same number. In this case, that number is X. Depending on how we multiply them, we may end up with our answer or AX + BX = CX. If that's how we want it, we can use the distributive property to factor out the X and end up with our answer. Hooray.