To solve the expression $\frac{14}{15} \div 1 \frac{2}{5}$, let's follow these steps:

Step 1: Convert the mixed number to an improper fraction.

The mixed number $1 \frac{2}{5}$ can be converted as follows:

$1 \frac{2}{5} = \frac{5 \times 1 + 2}{5} = \frac{7}{5}$

Step 2: Rewrite the division as multiplication.

Dividing by a fraction is the same as multiplying by its reciprocal:

$\frac{14}{15} \div \frac{7}{5} = \frac{14}{15} \times \frac{5}{7}$

Step 3: Multiply the fractions.

Now, multiply the numerators and denominators:

$\frac{14}{15} \times \frac{5}{7} = \frac{14 \times 5}{15 \times 7} = \frac{70}{105}$

Step 4: Simplify the fraction.

Simplify $\frac{70}{105}$ by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 35:

$\frac{70 \div 35}{105 \div 35} = \frac{2}{3}$

Final Answer:

The result of $\frac{14}{15} \div 1 \frac{2}{5}$ is $\frac{2}{3}$.

Would you like more details or have any questions about the solution?

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Here are 5 related questions:

1. How do you find the reciprocal of a fraction?
2. What is the process for multiplying two fractions?
3. How do you simplify a fraction after multiplication?
4. What are mixed numbers and how are they converted to improper fractions?
5. How do you divide fractions step-by-step?

Tip: Always simplify fractions before multiplying or dividing to make calculations easier!