# Thread: Simplifying 1 - (x/y)

1. ## Simplifying 1 - (x/y)

Hi all, in my workbook I am transforming a formula and I've transformed part of it to $\displaystyle 1-\frac{x}{y}$ but in the workbook it as gone one step further and simplified it to $\displaystyle \frac{y-x}{y}$ but I can't quite see how it has got to that. Would someone mind helping me out please? Thanks, John

2. ## Re: Simplifying 1 - (x/y)

John

substitute 1 as a fraction y/y and then subtract.... it is simple....

3. ## Re: Simplifying 1 - (x/y)

Thanks for your reply and my apologies but I don't understand why 1 would be substituted with y/y (although I'm happy with the subtraction after that)

4. ## Re: Simplifying 1 - (x/y)

You make the denominators equal..

........................$\displaystyle 1 - \frac{x}{y}$

........................$\displaystyle =\frac{1 * y}{y}- \frac{x}{y}$

........................$\displaystyle = \frac{y}{y}- \frac{x}{y}$

........................$\displaystyle = \frac{y-x}{y}$

Does that answer you question? c:

5. ## Re: Simplifying 1 - (x/y)

Great, I get it now. Thanks so much for your help both of you.

John

6. ## Re: Simplifying 1 - (x/y)

Originally Posted by johncassell
Great, I get it now. Thanks so much for your help both of you.

John
you don't get it.

and n=n/1

Now you can fish.

7. ## Re: Simplifying 1 - (x/y)

Originally Posted by Hartlw
Now you can fish.
Fishing for compliments eh? :P

Seriously though - the reason that rule holds is because the OP needs to understand that in order to add two fractions, they need to have common denominators. Once you realise the LCD is y, it's easy

8. ## Re: Simplifying 1 - (x/y)

Originally Posted by Prove It
Fishing for compliments eh? :P

Seriously though - the reason that rule holds is because the OP needs to understand that in order to add two fractions, they need to have common denominators. Once you realise the LCD is y, it's easy
The goal is not to solve a particular problem by doing something, but to learn something by doing it in the right way:

What do you want to do? Add two fractions.
What is the definition of fraction addition?

And yet, I admit the definition obscures the principle which is the source of the definition, and you have a point; I might even go so far as to say you are right. So:

What do you want to do? Add two fractions.
How do you add fractions? Reduce them to a common denominator.

SUMMARY:

1) What is the problem?
2) What is the relevant definition OR principle?

I stand corrected. Thanks Prove It and apologies to Lexadis who did state the principle.

9. ## Re: Simplifying 1 - (x/y)

Originally Posted by johncassell
Hi all, in my workbook I am transforming a formula and I've transformed part of it to $\displaystyle 1-\frac{x}{y}$ but in the workbook it as gone one step further and simplified it to $\displaystyle \frac{y-x}{y}$ but I can't quite see how it has got to that. Would someone mind helping me out please? Thanks, John
The OP didn't present a problem in addition of fractions. He wanted to know how you get from A to B, which MINOANMAN answered.

10. ## Re: Simplifying 1 - (x/y)

Originally Posted by Hartlw
The OP didn't present a problem in addition of fractions. He wanted to know how you get from A to B, which MINOANMAN answered.
Subtraction is addition (of negative numbers), whole numbers are fractions (with denominator of 1), and the "formula" used comes from the understanding that addition of fractions requires a common denominator. Everything that was posted was relevant.