need help for simplification rules

[vijaykn]

in this equation 10/x=40/100 why cant i simplify 10 and 100, please let me know the reasons and criteria for simplification, where should i use and where i shouldn't use.

 

[skeeter]

you can reduce the fraction 40/100 to 4/10 ... don’t know what you mean by “simplifying” 10 and 100

 

[Mackattack]

From my understanding, you can't simplify the 10 and 100 because you're not multiplying them. You only do the "cross thing" if you're multiplying them.

 

[pka]

in this equation 10/x=40/100 why cant i simplify 10 and 100, please let me know the reasons and criteria for simplification, where should i use and where i shouldn't use.

There are several ways to proceed. Here is one:
\(\dfrac{10}{x}=\dfrac{40}{100}\\1000=40x\)

 

[lookagain]

where should i use and where i shouldn't use.

You can also express it as:

\(\displaystyle \dfrac{1}{x} \ = \ \dfrac{4}{100}\)

 

[Steven G]

I 100% agree with look again. Now take reciprocals and what do you get?

Or you can reduce the right hand side and read off the answer.

 

[vijaykn]

the question i am asking here is what are the rules for simplification , is the above example known as right hand side = left hand side, why cannot i cancel a numerator on the right to the denominator ( RHS) on the left (LHS), I see that before cross multipying simplification can be done. Hope the question is clear now.

 

[vijaykn]

when i meant -a numerator on the right to the denominator ( RHS) on the left (LHS), it is 10 and 100