split - Algebra Problem of the Day-2

[DarnellRyan]

I know this is easier math, but I was having trouble solving problems like “4/15<<numerator) over 3/5ths<<<denominator) I couldn’t do it the way they showed me so I made up my own way to solve the problem. I took 4/15 (divided by “N”) = 3/5ths. I multiply 3/5ths on the right of equal sign by 5/3rds which moves 5/3rds left of equal sign. I multiple N on left side (because it were dividing on that side) to to get N to the right side of equal signs on opposite side of the fractions. So (4/15 x 5/3) = N . ) cross factor 5 and 15 which leaves 4/3rds x 1/3rd= N) Finish solving looks like N = 4/9th<<<fraction which is the correct answer. When the numerator fraction is smaller than Denominator you will divide ( 4/15 divided by N = 3/5) If the denominator is smaller than the numerator, you will multiply (I.e) 3/5ths over 1/4) you will do (3/5ths x N = 1/4).
I got so mad I couldn’t get it right, I came up with this way to solve the problem to make it easier for me. I thought it was cool, not sure about you but thank you for the time if you read it all

 

[Steven G]

Whenever you multiply (or divide) by 1, the value will not change. It may look different but the value did not change.

If for example you have \(\displaystyle \dfrac{\dfrac{3}{4}}{\dfrac{5}{7}}=\dfrac{\dfrac{3}{4}}{\dfrac{5}{7}}*1=\dfrac{\dfrac{3}{4}}{\dfrac{5}{7}}*\dfrac{\dfrac{7}{5}}{\dfrac{7}{5}}=\dfrac{ \dfrac{3}{4}*\dfrac{7}{5}}{1}=\dfrac{3}{4}*\dfrac{7}{5}=\dfrac{21}{20}\)

 

[topsquark]

Whenever you multiply (or divide) by 1, the value will not change. It may look different but the value did not change.

If for example you have \(\displaystyle \dfrac{\dfrac{3}{4}}{\dfrac{5}{7}}=\dfrac{\dfrac{3}{4}}{\dfrac{5}{7}}*1=\dfrac{\dfrac{3}{4}}{\dfrac{5}{7}}*\dfrac{\dfrac{7}{5}}{\dfrac{7}{5}}=\dfrac{ \dfrac{3}{4}*\dfrac{7}{5}}{1}=\dfrac{3}{4}*\dfrac{7}{5}=\dfrac{21}{20}\)

No complaints about the post, just a LaTeX note.

I would do one of two things here to make the fractions clearer:
\dfrac{ left ( \dfrac{3}{4} \right ) }{ \left ( \dfrac{7}{5} \right ) }
[imath]\dfrac{ \left ( \dfrac{3}{4} \right ) }{ \left ( \dfrac{7}{5} \right ) }[/imath]

or
\dfrac{ ^3 / _4 }{ ^7 / _5 }
[imath]\dfrac{ ^3 / _4 }{ ^7 / _5 }[/imath]

I haven't yet found a way to make that middle line longer to emphasize it.

-Dan

Follow-up: I just got a tip. Add a space on each internal fraction line:
\dfrac{ \; \dfrac{a}{b} \; }{ \; \dfrac{c}{d} \; }
[imath]\dfrac{ \; \dfrac{a}{b} \; }{ \; \dfrac{c}{d} \; }[/imath]