Final answer:
To divide 1\dfrac{1}{4} by 1\dfrac{2}{5}, convert the mixed numbers to improper fractions, find the reciprocal of the divisor, multiply the fractions, and simplify. The quotient in lowest terms is \dfrac{25}{28}.
Step-by-step explanation:
The student asked to divide and write the quotient in lowest terms for the problem 1\dfrac{1}{4} \div 1\dfrac{2}{5}. To solve this, we first need to convert both mixed numbers into improper fractions:
- 1\dfrac{1}{4} becomes \dfrac{5}{4}.
- 1\dfrac{2}{5} becomes \dfrac{7}{5}.
To divide fractions, we multiply the first fraction by the reciprocal of the second. So:
- \dfrac{5}{4} \div \dfrac{7}{5} is the same as \dfrac{5}{4} \times \dfrac{5}{7}.
Multiplying these fractions together, we get:
- \dfrac{5 \times 5}{4 \times 7} = \dfrac{25}{28}.
Since 25 and 28 have no common factors besides 1, the fraction \dfrac{25}{28} is already in its lowest terms.
Therefore, the quotient in lowest terms is \dfrac{25}{28}.