Changing 22 1/3% to a fraction: is there a formula?

[craneangl]

When you are converting a percentage like 22 1/3% to a fraction, do you just forget the percentage sign and treat it like any other mixed fraction, or is there a different formula for this? I am not sure how to do it.

Thank you!

 

[jonboy]

Do you mean changing into an improper fraction? If so there is no special formula for a percent, except calling the new fraction a percent of course.

Whenever you have a proper fraction in the form: \(\displaystyle \L\bold A \frac{b}{c}\) You multiply A*c+b and put it over the original c.

So for 22 1/3%:

\(\displaystyle \L\bold 22 \frac{1}{3}%\)

Multiply 3*22 and add 1.

\(\displaystyle \L\bold \frac{67}{3}%\)

 

[tkhunny]

What? The "%" adds another factor of 100.

22 1/3% = 67/3 % = 67/300

Check it out...67/300 = 0.223333333333... Yup.

 

[craneangl]

The problem is simply converting a percentage such as the one I suggested into a fraction. So would the final answer be 67/3?

 

[jonboy]

I would use that as my final answer because 67/300 is not converted yet as a percent.
BTW plz be more specific when you say "change into a fraction". Fortunatley I could read between the lines but be more specific and say "improper fraction/proper fraction/mixed number, etc."

Thank you.

 

[Mrspi]

Re: Changing a mixed fraction

OWhen you are converting a percentage like 22 1/3% to a fraction, do you just forget the percentage sign and treat it like any other mixed fraction, or is there a different formula for this? I am not sure how to do it.
Thanks

What if the problem had asked you to do this: convert 25% to a fraction

Wouldn't you say "Oh....% means 'out of 100,' so 25% means 25/100. And I can reduce that to 1/4. So, 25% as a fraction is 1/4."

Do the same thing for 22 1/3%:

(22 1/3) / 100

(67/3) / 100

Multiply both numerator and denominator by 3, and you'll get the answer given by TKHunny in an earlier post.

jonboy.....don't you agree?