How do you evaluate #6\frac { 7} { 11} - 6\frac { 2} { 6}#?

To multiply that, rewrite the mixed fractions as improper fractions.

Take the denominator of the mixed fraction, multiply it by the whole number and add the numerator. Whatever value you get becomes the numerator of the improper fraction over the denominator of the mixed fraction.

For #6(7)/11#, we multiply #11# by #6# and add the product to #7#

#(11*6)+7#

#66+7#

#73#

So our numerator is #73# over our denominator which is #11#

#:.#Our improper fraction for #6(7)/11# is #73/11#

For #6(2)/6#, we multiply #6# by #6# and add the product to #2#

#(6*6)+2#

#36+2#

#38#

So our numerator is #38# over our denominator which is #6#

#:.#Our improper fraction for #6(2)/6# is #38/6#

Now to the question;

#73/11-38/6#

We can only add and subtract fractions when they have the same denominator. We would have to get the #lcm# of #11# and #6#. That is #66#.

To make #11# = #66#, we multiply by #6#. Remember what you do the denominator, you do the same to the numerator.

#6/6*73/11=438/66#

To make #6# = #66#, we multiply by #11#. Remember what you do the denominator, you do the same to the numerator.

#11/11*38/6=418/66#

So since the denominators are the same, we subtract.

#438/66-418/66#

#(438-418)/66#

#20/66#

#(2xx10)/(2xx33)=(cancel(color(red)2)xx10)/(cancel(color(red)2)xx33#

#rArr10/33#