Answer:
To divide 3 3/10 by 1 4/7, we first need to convert both mixed numbers into improper fractions.
3 3/10 can be written as (3 x 10 + 3)/10 = 33/10
1 4/7 can be written as (1 x 7 + 4)/7 = 11/7
Now, we can rewrite the division problem as:
33/10 ÷ 11/7
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:
33/10 x 7/11 = (33 x 7)/(10 x 11) = 231/110
This fraction can be simplified to lowest terms by dividing both the numerator and denominator by their greatest common factor, which is 11:
231/110 ÷ 11/11 = (231 ÷ 11)/(110 ÷ 11) = 21/10
Therefore, the quotient of 3 3/10 ÷ 1 4/7 in lowest terms is equal to 21/10.