the quotient is the result after dividing one number by another :
quotient = x/y
the same applies, of course, when dividing 2 quotients, as each quotient is simply again a number.
when using fraction bars we have to represent both basic fractions.
draw a line that represents 1 unit.
under that line draw it again, but mark 12 equally sized parts as blocks of the whole 1 above. these represent the individual 1/12 parts. mark the first 10 of the 12 in a special way. they are the 10/12.
beneath that draw it again, but mark 6 equally sized parts as blocks of the whole 1 on the top. you will see that each of these 1/6 blocks covers 2 of the 1/12 blocks. now, mark the first 4 of the 6 in a special way. they are the 4/6.
and they are covering 8 of the 1/12 blocks. that means 8 of the 10 special marked blocks of 10/12.
a quotient between x and y simply means how often does y fit into x.
so, how often do the 8 covered blocks fit into the 10 total blocks of 10/12 ?
1 time (8 blocks) plus 2 blocks remainder.
that is 10 out of the covered 8 blocks, which means 10/8 times in total.
and how many groups of 2 blocks fit into 8 blocks ? 4.
so, 2 blocks represent ¼ of 8 blocks.
that means our quotient is
10/8 = 1 ¼ = 1.25
for another approach let's remember :
the 10 special blocks of the 10/12 block cover exactly 5 of the 1/6 blocks. and 8 of them cover the mentioned 4 blocks in the 1/6 row.
so,
10/8 = 5/4 = 1 ¼