Final answer:
To divide 1 2/5 by 1 3/10, convert both fractions to improper fractions, perform the division, and simplify the resulting fraction to its simplest form, which is 14/13.
Step-by-step explanation:
To divide 1 2/5 by 1 3/10, we need to convert both fractions to improper fractions and then perform the division.
1 2/5 as an improper fraction is (1 * 5 + 2) / 5 = 7/5.
1 3/10 as an improper fraction is (1 * 10 + 3) / 10 = 13/10.
Now we can divide: (7/5) / (13/10) = (7/5) * (10/13) = 70/65.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor is 5. Dividing 70 by 5 gives us 14, and dividing 65 by 5 gives us 13.
Therefore, 1 2/5 divided by 1 3/10 in its simplest form is 14/13.