Understanding the Distributive Property in Simplifying Expressions

[A.J.710]

This question is the very end of a large problem that I really can't figure out. It's an online course and the computer keeps saying the same thing so I am getting confused.

It says simplify 1-(1-sinθ)

My answer: -sinθ
Computer's answer: sinθ

From what I understand, it would come out to -sinθ but the computer keeps saying its positive sinθ. I know I am probably overlooking something and that is why I am asking here for advice. I am just trying to understand what I am missing.

 

[QuantumCurt]

The negative in front of the parentheses distributes in, and eliminates the parentheses, leaving you with 1-1+sin x, recalling that a negative times a negative is a positive. The 1 and the -1 cancel, leaving you with a positive sin x.

 

[A.J.710]

Perfect! Thank you. LOL see sometimes you look over the easy things in math :) I have been doing this online course for 14 hours straight today so my brain is pretty much fried.

The negative in front of the parentheses distributes in, and eliminates the parentheses, leaving you with 1-1+sin x, recalling that a negative times a negative is a positive. The 1 and the -1 cancel, leaving you with a positive sin x.

 

[QuantumCurt]

I know what you mean! 9/10 of the mistakes I make in math come down to some simple little computational/arithmetic error.

 

[jedishrfu]

I know what you mean! 9/10 of the mistakes I make in math come down to some simple little computational/arithmetic error.

I'd say it was more of a conceptual error in not being comfortable with the distributive law when subtraction is applied after all its really a contraction of 1 + (-1)*(1 - sin theta)

Its really good to be able to categorize your arithmetic mistakes so you identify the underlying cause and fix it. If you just shrug it off then you'll keep doing the same mistakes over and over again.

 

[micromass]

Its really good to be able to categorize your arithmetic mistakes so you identify the underlying cause and fix it. If you just shrug it off then you'll keep doing the same mistakes over and over again.

Agreed 100%. Categorizing mistakes has been extremely helpful to me when I was new to math!

 

[QuantumCurt]

Yeah, that is more of a conceptual error. The distributive law is one that many people have trouble with. I tutor a lot of elementary/intermediate algebra students, and that's one of the parts that they seem to have trouble with most often, but only when negative signs are involved. I remember learning the basic properties of algebra way back in the day(distributive property, zero factor property, multiplicative inverse property, etc) and feeling that it was completely pointless to learn them. Turns out that those properties are actually very valuable knowledge to hang on to.

 

[jedishrfu]

The error categorizing is critical. My brother was once very frustrated with his math. It turned out that while he checked his work his check was always flawed which caused him to go back and change the answer. This distributive law issue if it didn't come up in the problem would come up in the check causing the error that sent him to the dark side.