Algebra

 Beverly's daughter is in the ninth grade, learning algebra.  Came to me for help on a problem:

            Simplify 4A + 5B - (3A +2B)

Ok,    A + 3B

My teacher said that's not right.  She said the answer was A +7B

Well, no, the minus sign changes all the signs inside the parentheses.

Why?

Because it's the rule.

Why?

Because otherwise it doesn't make sense.  You can't change 3A to -3A and not change 2B to -2B.

But...

I'll prove it.  Put small numbers in for A and B and calculate the result of the original expression and the simplified one.  They have to match, right?

Why?

Let's say A = 2 and B = 3.  4A + 5B - (3A +2B) becomes 8 + 15 - (6 + 6) = 11

And, A + 3B becomes 2 + 9 = 11.   Your teacher's solution of A +7B would give 2 + 21 = 23.  Clearly not right.

I don't think she's going to like that.

Show her how to sub in small numbers.  It will prove it to her.

*Next day*. What did your teacher say?  She was gone today.

*Next day*. What did your teacher say?  I didn't tell her.

*Next day*. What did your teacher say?  I didn't tell her.

My offer to write a letter to the teacher is still pending...



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