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!

Learn to solve the expression 14/15 ÷ 1 2/5 by converting mixed numbers into improper fractions, multiplying by the reciprocal, and simplifying the result. A detailed, step-by-step guide suitable for students in Grades 6-8.

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