how is 20/3 % = 6 2/3% ?

20/3 = 18/3 + 2/3 = 6 2/3
7/3 = 6/3 + 1/3 = 2 1/3

It's simply converting improper fractions to complex fractions.

At the first step, forget the percentage.

20/3 is the same as "20 divided by 3"

If you divide 20 by 3, you get 6, with a remainder of 2
(because 3*6 = 18)

You would write this as
20/3 = 6 + 2/3 = "six and two thirds" = 6 2/3

If these were apples, you would write

20/3 apples = 6 2/3 apples

But they are "percentages" so you write

20/3 % = 6 2/3 %

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A percentage is just a fancy way to write a fraction over 100.

20/3 % is the same as (20/3) / 100 = 20/300

6 2/3 % is the same as
(6 + 2/3) / 100 = 6/100 + 2/300 = 18/300 + 2/300 = 20/300
(same value)

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6 and 2/3 can also be written as 6.666666...

If you divide this number by 100, you move the decimal left by two places

"6 and 2/3" divided by 100 = 6.6666... / 100 = 0.066666...

Therefore, 6 2/3 % is also equal to 0.0666666...

(the 6s go on forever, but my fingers get tired of typing 6s well before I get to "forever")

It's the same thing
20/3 and 6 2/3 are the same thing. It's just that 20/3 is improper and 6 2/3 is mixed. There is no solution, this is just a statement (yeah, call it an equation by definition but it's just saying that the first number equals the second).

just think of converting a number to an improper fraction

20/3 = 6 2/3

There's no need for a solution as such, what you have stated is the solution. 20/3 is 6 2/3, it's also 6.66666...

7/3 is the same thing as 2 1/3.

20/3 and 7/3 are called top heavy fractions (or improper fractions) where the numerator (number on the top) is bigger than the denominator (number on the bottom).

In the case of 20/3 if you divide 20 by 3 you get 6 (6x3=18 remainder 2, the remainder 2 bit is 2 thirds).

In the case of 7/3 it's the same thing 7 will divide into 3 twice (2x3=6 with 1 remainder) the one remainder is the one third.

Hope that helps.

If you want more practice with fractions here's a cool website.

http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/fractions/simplifyingfractions/factsheet.shtml

18 / 3 = 6

6 2/3
=6 + 2/3
=18 / 3 + 2/3
=18/3 + 2/3
=(18 + 2)/3
=20/3

because 20/3 = 6 2/3 so their equal in percentage too

20 / 3 by simple division how many whole 3s we can get from 20. If you know multiplication table of 3 then you know 6 x 3 = 18 if you take the 18 away from 20 there will be 2 left. Obviously 3 can't divide the 2 therfore, we leave the notation like 20 has 6 of whole 3s and a reminder2 that is simply written as 6 2/3

Consider the fraction 20 / 3.
It can be simplified, by 'dividing the bottom into the top' to become 6 and 2 remainder.
The "2 remainder" is 2 / 3: we divided by 3.
Hence "20 / 3" is the same thing as 6 and 2/3 . . . in words "six and two-thirds".
Thus "20 / 3 per cent" = "6 and 2 / 3 percent" . . . your question.

O.K. ?
I think you were thinking about this too hard! It's easy to 'think too hard' sometimes in maths!

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Let's have a look at the next example - hopefully easier for you to grasp, now . . .

"seven over three": divide "three" into "seven": you get "two", remainder "one". That "one" is "one third", since we were dividing by "three". Yes?
So you now have "two" plus "one third" . . . . . 2 1/3, when written in "numbers".

I can see that you've got it now! Yippee!
{Did you know that I was 'advanced telepathic'? ;-) And a bit nutty! Mathematicians frequently are!}
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