Question 554167
A percent is really a ratio, and a ratio is really a fraction, or a decimal number. Let me show you with an example.
EXAMPLE:
Let's say you want trying to calculate 6% tax on a $400 purchase.
6% is 6 out of every hundred.
As a ratio (or fraction) that is
6% = {{{6/100}}} (Sometimes they write ratios as 6:100, but I find the little dots hard to read, and sometimes confuse ":" and ";").
To calculate the tax in your head, you would figure out how many times $100 fits into the price by dividing by $100 to get 4 times. Then you would multiply that times $6, which is the tax on each $100. That can be calculated as
${{{400}}} x {{{6/100}}} = ${{{24}}} or $400 x 0.06 = $24
There are many ways to write the same number:
{{{24/400}}} = {{{6/100}}} = {{{3/50}}} = {{{1&1/2/25}}} = {{{0.06}}}
Those are equivalent ways to write 6% as a ratio, or a fraction, or a decimal number.
By multiplying times the same number both parts of the ratio (top and bottom), you can transform one way of expressing the ratio into an equivalent expression meaning the same ratio. 
You could also divide by the same number both parts to get an equivalent expression, meaning the same ratio.
The ratio {{{1&1/2/25}}} is a ratio but not a fraction, because {{{1&1/2}}} is not an integer. Multiplying top and bottom parts by 2, we get the equivalent expression {{{3/50}}}, which is a fraction.
{{{24/400}}}, {{{6/100}}}, {{{3/50}}} are ratios and fractions. They are the same number expressed in different ways.
The one with the smallest top and bottom parts (numerator and denominator) is said to be the simplest form, or to be "in simplest terms" or "in lowest terms.
If they ask you to simplify a fraction, you try to find a number that will divide numerator and denominator to make an equivalent fraction.
The fraction {{{24/400}}} could be simplified to {{{6/100}}} and/or to {{{3/50}}}.
However, there is no number that will evenly divide both 3 and 50, so {{{3/50}}} is the simplest fraction that expresses that ratio.
EXTRA:
Numbers that can be expressed as ratios are called rational. They include the fractions, an integers like {{{7=14/2=21/3}}}.
YOUR PROBLEM:
{{{58&1/2}}}% = {{{58&1/2/100}}} = {{{117/200}}}
Because 117= 3 x 3 x 13, and 200 = 2 x 2 x 2 x 5 x 5,
they do not have any common factor.
There is no number that we could use to divide 117 and 200 to get a fraction with smaller numerator and denominator.
Believe it or not, 117/200 is the simplest fraction meaning 58 1/2%.