# Thread: Having some trouble with Properties of Equality...

1. ## Having some trouble with Properties of Equality...

Well, I've read them. I know what they all state. But I don't get their application.

For reference, this is what my text lists them as:
Addition - If A=B, then A+C = B+C
Subtraction - If A=B, then A-C = B-C
Multiplication - If A=B, then AB=BC
Division - If A=B and C =/= 0, then A/C = B/C
Substitution - If A=B, then B can be used for A in any circumstance.
Symmetry - AB=BA
Transitive - If A=B and B=C, then A=C
Reflexive - AB=AB

...That said, I don't really get their usage.
Here's the segment on them from a recent test I got back, along with my answers. I missed 13, 14, and 16. My answers are bold, and my comments are italicized.

12. If JK = PQ and PQ = ST, then JK = ST. Transitive.
13. If AB + CD = EF + CD, then AB = EF. Addition. I don't get where I went wrong here.
14. AB = AB. Transitive. This is purely me forgetting about Reflexive, and forgetting whether Transitive was the A=A one or the A=B/B=C:A=C one.
15. If AB = CD, then CD = AB. Symmetric.
16. If AB - CD = EF - CD, then AB = EF. Subtraction. Same song as 13. Not sure where I went wrong.

I got the rest of the test right, except for one problem I just made an easy-to-fix stupid mistake on. So these alone are causing me problems. Help, please?

2. You mixed up between the two questions.

13. If a - c = b - c, then a = b. This is addition property of equality because you added c to both sides which in turn cancelled the other c yielding a = b.

$\displaystyle a - c = b - c$

$\displaystyle \Rightarrow a - c + c = b - c + c$

$\displaystyle \Rightarrow = a = b$

16. If a + c = b + c, then a = b. This is subtraction property of equality because you subtracted c from both sides to get a = b.

$\displaystyle a + c - c = b + c - c$

$\displaystyle \Rightarrow a = b$

You thought that you should classify the hypothesis as addition or subtraction, but this is not what they asked you for. They wanted you to know which property did you use to come up to the conclusion that a = b. Understand the question completely before attempting to solve it next time.