Would anyone care to explain to me.....

[solarbeam2021]

... how this:


Became this?


The guy said "..divide both sides by 'b' and both sides by 'x'."

 

[solarbeam2021]

Got it.
Apparently there's something called "fraction rule" that states: [MATH]b/c/a = b/c*a[/MATH]

 

[Harry_the_cat]

When you divide both sides by b, you get
\(\displaystyle \frac{ax}{b}= 100-x\)
Now divide both sides by x

 

[Dr.Peterson]

Got it.
Apparently there's something called "fraction rule" that states: [MATH]b/c/a = b/c*a[/MATH]

You need to be careful with order of operations; what you mean is [MATH](b/c)/a = b/(c*a)[/MATH].

The basic rule is that dividing by a is the same as multiplying by 1/a; so you multiply the denominator: `(b/c)/a=b/c*1/a=b/(ca)`

To put it another way, dividing by a and then by x is the same as dividing all at once by (ax).

 

[HallsofIvy]

I would have interpreted "b/c/a= b/c*a" as "b/(c/a)= (b/c)*a"! Use parentheses!

 

[Steven G]

There is something called the main division line which is quite important.

Consider[math]\dfrac{\frac{100}{10}}{2} = \dfrac{10}{2} = 5[/math] while [math]\dfrac{100}{\frac{10}{2}} = \dfrac{100}{5} = 20[/math].

Note that I divided the same three numbers in the same order but got different answers! The longer division line is the main division line.

The first problem is the result of 100/10 divided by 2 while the 2nd problem is 100 divided by the result of 10/2.