Answer by Anonymous Computer for Meaning of $\frac{x-y}{y}$ versus...
Let's assume our fraction $\dfrac{x-y}{y}$ equals $a$.$$\frac{x-y}{y}=a$$Multiplying by $y$ on both sides...$$x-y=ay$$Isolating $x$...$$x=ay+y$$Factoring the right hand side:...$$x=y(a+1)$$Dividing by...
View ArticleAnswer by Kasper for Meaning of $\frac{x-y}{y}$ versus $\frac{x}{y}-1$
Hint: What would you do if the question was:$$\frac{x-2}{2}$$or $$\frac{x-3}{3}$$or $$\frac{x-4}{4}$$etc. Try to find a pattern.
View ArticleAnswer by Posted by another Tim for Meaning of $\frac{x-y}{y}$ versus...
I would like to take a crack at explaining this...Using the distributive property, we can rearrange the equation... $$\frac{x-y}{y} \rightarrow \frac{x-y}{y..y} \rightarrow\frac{x}{y}-\frac{y}{y}$$ We...
View ArticleAnswer by Peter - Reinstate Monica for Meaning of $\frac{x-y}{y}$ versus...
As others mentioned, it's because of the "distributive property" of the operation. But why does the distributive law apply? It's more intuitive for a sum than for a difference, and I always like a...
View ArticleAnswer by Joao for Meaning of $\frac{x-y}{y}$ versus $\frac{x}{y}-1$
multiply both expressions by $y$ so that $$\frac{x-y}{y}$$ becomes $x-y$ and $$\frac{x}{y}-1$$ becomes $y(\frac{x}{y}-1)=x-y$.
View ArticleAnswer by David for Meaning of $\frac{x-y}{y}$ versus $\frac{x}{y}-1$
If you want an informal answer rather than an algebraic proof, see if this helps.Suppose you have $x$ lollies (or sweets, or candies, depending which country you are in) to be shared equally among $y$...
View ArticleAnswer by SOULed_Outt for Meaning of $\frac{x-y}{y}$ versus $\frac{x}{y}-1$
Since there is subtraction in the numerator: $$\frac{x-y}{y}=\frac{x}{y}-\frac{y}{y}=\frac{x}{y}-1$$
View ArticleAnswer by Ben Grossmann for Meaning of $\frac{x-y}{y}$ versus $\frac{x}{y}-1$
It comes down to the distributive law:$$\frac{x-y}{y} = \frac{1}{y}(x-y) = \frac 1y x - \frac 1y y = \frac xy - 1$$
View ArticleMeaning of $\frac{x-y}{y}$ versus $\frac{x}{y}-1$
I'm trying to understand what is probably a fairly simple math concept, but this is escaping me for some reason. Why are the results of these two expressions equal? Thanks for any...
View Article
