1. ## simple fraction question

ok so does

$\displaystyle 1 \frac {2x^2+y^2}{y}$

equal
$\displaystyle 1 \frac {2x^2+y}{1}$

just confused over the the whole 1.. can i simplify it anymore or multiply the 1 into the fraction some how?

2. when you multiply anything by 1, nothing happens...so you can cancel that 1 off...

and the 1st equation doesn't equal the second...the first equation is about as simple as it gets (once you've cancelled the 1)

3. Originally Posted by Jbuckham
ok so does

$\displaystyle 1 \frac {2x^2+y^2}{y}$

equal
$\displaystyle 1 \frac {2x^2+y}{1}$

just confused over the the whole 1.. can i simplify it anymore or multiply the 1 into the fraction some how?
No. Because y is not a common factor in the numerator. If it was $\displaystyle 1 \frac {2x^2 {\color{red}y} +y^2}{y}$ then yes it would.

4. Originally Posted by mr fantastic
No. Because y is not a common factor in the numerator. If it was $\displaystyle 1 \frac {2x^2 {\color{red}y} +y^2}{y}$ then yes it would.
but isn't $\displaystyle \frac {y^2}{y} = y$

ohhh the y has to be involved in all the factors.. hence the common factor comment.. i understand
thank you

5. Originally Posted by shabz
when you multiply anything by 1, nothing happens...so you can cancel that 1 off...

and the 1st equation doesn't equal the second...the first equation is about as simple as it gets (once you've cancelled the 1)
I'm sorry I'm confused here
see when you have $\displaystyle 1 \frac{1}{2}$ that equals $\displaystyle \frac{3}{2}$
which is not $\displaystyle 1* \frac{1}{2}$

6. Originally Posted by Jbuckham
I'm sorry I'm confused here
see when you have $\displaystyle 1 \frac{1}{2}$ that equals $\displaystyle \frac{3}{2}$
which is not $\displaystyle 1* \frac{1}{2}$
This is just a really unfortunate, ambiguous notation that should never have gone into use. Typically in mathematics, placing one term next to a fraction implies multiplication. But the same is occasionally done to indicate mixed fractions, hence the confusion. For clarity, you should write an explicit plus sign to indicate addition, or parentheses to indicate multiplication.

$\displaystyle 1+\frac{2x^2+y^2}y$

$\displaystyle =\frac yy+\frac{2x^2+y^2}y$

$\displaystyle =\frac{2x^2+y^2+y}y,$

which is not, in general, equal to

$\displaystyle 1+2x^2+y.$