Thread: help! how to deal with negative fractions?

This problem completely confuses me as it had negative fractions. The answer that I worked out is different from the answer key.

Simplify:

(3a/-b) (b^2/6b) (b/-a)

= (3/6) (a/-a) (b^3/-b^2)

= (1/2) (-a^0) (-b^1)

= (1/2) (1) (-b)

= -b/2

The answer key gives +b/2 as the answer.

Should the negative sign in (3a/-b) be applied to 3 as well, such that step 2 would be:

(-3/6) (a/-a) (b^3/-b^2)

By having a -3, I could simplify the expression to +b/2. Does this mean that the negative sign in -b should be applied to 3 as well?

Please help, I can't find any resource that discusses simplifying negative fractions. Thanks in advance.

-a^0 does not equal 1, it equals -1

remember it really says: -1a^0

thus: -1(a^0)

then: -1(1)

finally: -1

That was quick. Thanks!

I didn't know what -a^0 is. So I put in something like -22^0 in the calculator and it gives me a 1, so I thought -a^0 is 1. Your proof of -a^0 is equal -1 certainly helps.

(3a/-b) (b^2/6b) (b/-a)

= (3/6) (a/-a) (b^3/-b^2)

I'm not good in math, my head is still spinning about negative fractions. Since the mistake is in -a^0, I think the (3/6) in the second step is correct. It should not be (-3/6). It sounds silly to ask this, I'm thinking in terms of other questions, Is that right? Thanks again.

Originally Posted by shenton

That was quick. Thanks!

I didn't know what -a^0 is. So I put in something like -22^0 in the calculator and it gives me a 1,

That should not be the case.....-22^0 = -1 too

Maybe the calculator thinks (-22)^0 = 1
but -22^0 = -1

Originally Posted by classicstrings

Maybe the calculator thinks (-22)^0 = 1
but -22^0 = -1

I am at loss now.

My calculator, Casio fx-550s computes -22^0 = 1

This web based exponent calculator, Exponential Expression Calculator computes -22^0 = 1

It is hard to imagine this one as it is in the negative sign.

Originally Posted by shenton

I am at loss now.

My calculator, Casio fx-550s computes -22^0 = 1

This web based exponent calculator, Exponential Expression Calculator computes -22^0 = 1

It is hard to imagine this one as it is in the negative sign.

I'm not sure...

See picture... top on is TI-84 Plus, bottom CASIO fx-82MS

Originally Posted by shenton

I am at loss now.

My calculator, Casio fx-550s computes -22^0 = 1

This web based exponent calculator, Exponential Expression Calculator computes -22^0 = 1

It is hard to imagine this one as it is in the negative sign.

The web based calculator should get 1 as it is really calculating (-22)^0

Your calculator should require brackets to get 1 and get -1 without them

Originally Posted by shenton

I'm not good in math, my head is still spinning about negative fractions. Since the mistake is in -a^0, I think the (3/6) in the second step is correct. It should not be (-3/6). It sounds silly to ask this, I'm thinking in terms of other questions, Is that right? Thanks again.

All of the work in your original post except -a^0 was correct

Originally Posted by shenton

That was quick. Thanks!

I didn't know what -a^0 is. So I put in something like -22^0 in the calculator and it gives me a 1, so I thought -a^0 is 1. Your proof of -a^0 is equal -1 certainly helps.

(3a/-b) (b^2/6b) (b/-a)

= (3/6) (a/-a) (b^3/-b^2)

I'm not good in math, my head is still spinning about negative fractions. Since the mistake is in -a^0, I think the (3/6) in the second step is correct. It should not be (-3/6). It sounds silly to ask this, I'm thinking in terms of other questions, Is that right? Thanks again.

Originally Posted by classicstrings

That should not be the case.....-22^0 = -1 too

Maybe the calculator thinks (-22)^0 = 1
but -22^0 = -1

Originally Posted by Glaysher

The web based calculator should get 1 as it is really calculating (-22)^0

Your calculator should require brackets to get 1 and get -1 without them

This is why you never trust calculators if you can do the problem yourself! (Just one of my many "Rules to Live By" that my Math students hate me for.)

-Dan

Originally Posted by topsquark

This is why you never trust calculators if you can do the problem yourself! (Just one of my many "Rules to Live By" that my Math students hate me for.)

-Dan

I agree with your math students

Originally Posted by classicstrings

I'm not sure...

See picture... top on is TI-84 Plus, bottom CASIO fx-82MS

Wow! This is interesting. Maybe the person who can solve this will win the Nobel prize.

Thanks, anyway for coming in.

Originally Posted by Quick

All of the work in your original post except -a^0 was correct

Thanks, Quick for for verifying and correcting my work.

Originally Posted by shenton

Wow! This is interesting.

The reason for this discrepenacy is based on the way the calculator takes an operation. His calculator computes,
-(22)^0=-(1)=-1
The online calculator computes,
(-22)^0=1

Maybe the person who can solve this will win the Nobel prize.

First, it is a matter of definition of how to define the zero exponent, it cannot be proved to be correct, thus there is no breakthrough.

Second, there is no such thing as a Nobel prize for mathematics. Because Nobel believed that math does not affect society (which is true). Alternatively, there is a legend that a mathematicion had adultery with his wife, which is probably false. Because for one thing, Nobel never did have a wife.

Originally Posted by shenton

Wow! This is interesting. Maybe the person who can solve this will win the Nobel prize.

Thanks, anyway for coming in.

I would just like to say that:

(-22)^0=1

and

-22^0=-1

this has been long established and isn't debatable. Notice that online calculator has paranthesis around what you type.