Post History
#4: Post edited
by
Chgg Clou
·
2021-08-13T07:04:11Z (over 3 years ago)
How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(c - d)}{{\color{red}{-}}(b - a)} \equiv \dfrac{c - d}{b - a}$?
- How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \equiv \dfrac{b - a}{d - c}$?
I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's [intuit subtraction as facing backward, and the negative sign as backward steps](https://betterexplained.com/articles/subtracting-negative-numbers/). How does this intuition assist us to intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(c - d)}{{\color{red}{-}}(b - a)} \equiv \dfrac{c - d}{b - a}$?- > Ah! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing).
- >
- > 
- >
- > In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). You get the idea.
- I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's [intuit subtraction as facing backward, and the negative sign as backward steps](https://betterexplained.com/articles/subtracting-negative-numbers/). How does this intuition assist us to intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \equiv \dfrac{b - a}{d - c}$?
- > Ah! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing).
- >
- > 
- >
- > In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). You get the idea.
#3: Post edited
by
Chgg Clou
·
2021-08-13T07:03:22Z (over 3 years ago)
How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{\color{red}{-}(c - d)}{\color{red}{-}(b - a)} \equiv \dfrac{c - d}{b - a}$?
- How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(c - d)}{{\color{red}{-}}(b - a)} \equiv \dfrac{c - d}{b - a}$?
I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's [intuit subtraction as facing backward, and the negative sign as backward steps](https://betterexplained.com/articles/subtracting-negative-numbers/). How does this intuition assist us to intuit $\dfrac{a - b}{c - d} \equiv \dfrac{\color{red}{-}(c - d)}{\color{red}{-}(b - a)} \equiv \dfrac{c - d}{b - a}$?- > Ah! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing).
- >
- > 
- >
- > In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). You get the idea.
- I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's [intuit subtraction as facing backward, and the negative sign as backward steps](https://betterexplained.com/articles/subtracting-negative-numbers/). How does this intuition assist us to intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(c - d)}{{\color{red}{-}}(b - a)} \equiv \dfrac{c - d}{b - a}$?
- > Ah! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing).
- >
- > 
- >
- > In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). You get the idea.
#2: Post edited
by
Chgg Clou
·
2021-08-13T07:02:30Z (over 3 years ago)
How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{c - d}{b - a}$?
- How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{\color{red}{-}(c - d)}{\color{red}{-}(b - a)} \equiv \dfrac{c - d}{b - a}$?
I'm not asking about algebra here. Undeniably, $\dfrac{a - b}{c - d} \equiv \dfrac{\color{red}{-}(c - d)}{\color{red}{-}(b - a)} \equiv \dfrac{c - d}{b - a}$. But how can I intuit this? If helpful, let's [intuit subtraction as facing backward, and the negative sign as backward steps](https://betterexplained.com/articles/subtracting-negative-numbers/).- > Ah! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing).
- >
- > 
- >
- > In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). You get the idea.
- I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's [intuit subtraction as facing backward, and the negative sign as backward steps](https://betterexplained.com/articles/subtracting-negative-numbers/). How does this intuition assist us to intuit $\dfrac{a - b}{c - d} \equiv \dfrac{\color{red}{-}(c - d)}{\color{red}{-}(b - a)} \equiv \dfrac{c - d}{b - a}$?
- > Ah! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing).
- >
- > 
- >
- > In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). You get the idea.
#1: Initial revision
by
Chgg Clou
·
2021-08-13T07:01:36Z (over 3 years ago)
How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{c - d}{b - a}$?
I'm not asking about algebra here. Undeniably, $\dfrac{a - b}{c - d} \equiv \dfrac{\color{red}{-}(c - d)}{\color{red}{-}(b - a)} \equiv \dfrac{c - d}{b - a}$. But how can I intuit this? If helpful, let's [intuit subtraction as facing backward, and the negative sign as backward steps](https://betterexplained.com/articles/subtracting-negative-numbers/).
> Ah! The addition/subtraction tells us which way to face, and the positive/negative tells us if our steps will be forward or backward (regardless of the way we're facing).
>
> 
>
> In a sense, the addition/subtraction acts as a verb ("face forward" or "face backward"), and the positive/negative acts as an adjective ("regular steps" or "backwards steps"). Or maybe it's an adverb, modifying how we walk (walk forwardly, walk backwardly). You get the idea.