How do you simplify #\frac { 13} { 1+ \frac { 6} { 7} }# and write it as a single fraction?

1 Answer
Mar 26, 2017

The first method is to multiply the numerator and denominator of the larger fraction both by #7#:

#13/(1+6/7)=(7(13))/(7(1+6/7))=91/(7(1)+7(6/7))=91/(7+6)=91/13=7#

The second method is to first simplify the denominator as a single fraction, then recall that dividing is the same as multiplying by the reciprocal:

#13/(1+6/7)=13/(7/7+6/7)=13/(13/7)=13xx7/13=7#