What is the quotient in ##2 4/7 -: 1 3/6##?

##2 4/7 ÷1 3/6=1 5/7##

When you divide mixed fractions you first convert them to improper fractions. Further, dividing by a number ##a/b## is equivalent to multiplying by its reciprocal i.e. for dividing by ##a/b##, you multiply by ##b/a## i.e. numerator and denominators reversed. Hence,

##2 4/7 ÷1 3/6##

= ##(2×7+4)/7÷(1×6+3)/6##

= ##18/7÷9/6##

= ##18/7×6/9##

= ##(2cancel18)/7×6/(1cancel9)##

= ##(2×6)/7##

= ##12/7=(1×7+5)/7##

= ##1 5/7##