I cannot do this problem.
Question:
0.7 = s/335 - s/5300
Find s.
do I do it as a quadratic or how else.
Thanks for help.
Or....
just multiply both sides by 335 and then multiply both sides by 5300
as the sides will remain equal.
$\displaystyle 0.7=\frac{s}{335}-\frac{s}{5300}$
$\displaystyle 0.7(335)=s-\frac{335s}{5300}$
$\displaystyle 0.7(335)(5300)=5300s-335s=4965s$
$\displaystyle 1242850=4965s$
$\displaystyle s=\frac{1242850}{4965}$
$\displaystyle 0.7=\frac{s}{335}-\frac{s}{5300}$
$\displaystyle 0.7=\frac{5300 \times s}{335 \times 5300}-\frac{335 \times s}{5300 \times 335}$
$\displaystyle 0.7=\frac{5300 \times s - 335 \times s}{335 \times 5300}$
$\displaystyle 0.7=\frac{s(5300 - 335)}{335 \times 5300}$
$\displaystyle 0.7=\frac{4965s}{1775500}$
$\displaystyle 0.7 \times 1775500=4965s$
$\displaystyle \frac{0.7 \times 1775500}{4965}=s$
$\displaystyle s \approx 250.322 $
Does it make sense now ?
If you have
$\displaystyle \frac{3}{5}-\frac{2}{5}=x$
then you can just multiply both sides by 5 to get 3-2=5x
It's the same as combining the fractions to get $\displaystyle \frac{3-2}{5}=x$
You can either combine the fractions or just multiply both sides by the denominators.
$\displaystyle x=\frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}= \frac{5}{6}$
$\displaystyle 2x=1+\frac{2}{3}$
$\displaystyle 6x=3+2=5$
is another way.
If x=5, then 2x=10 by multiplying both sides by 2, they are still equal and saying the same thing.
5=5, 5(2)=5(2), (3+2)=5, 2(3+2)=2(5)
If two sides are the same, then if you multiply all terms of both sides
by the same number, they will still be equal.
You should get used to adding fractions, so that it becomes easy,
however, multiplying by the denominators in this case is faster.
Consider $\displaystyle \frac{3}{5}$. This is the same as $\displaystyle \frac{3 \times 7}{5 \times 7}$ (since the seven cancels out). This trick allows us to set two different fractions to the same denominator, in order to add them easily.
Note : you are not actually doing anything to the equation by multiplying by 335 inside the fraction : you are only rewriting a fraction in a different form (but it is equivalent) to make it simpler to add. Therefore, since the equation is left unchanged, doing anything to the other side would be superfluous. Simple example :
$\displaystyle \frac{3 \times 7}{5 \times 7} = \frac{3}{5} \times \frac{7}{7} = \frac{3}{5} \times 1 = \frac{3}{5}$
See ? It is basically equivalent to multiplying the fraction by 1, but adding multiplicative information to allow fraction addition. Since multiplying by 1 does not change anything, there is nothing to change on the other side of the equation