To solve the expression \( \frac{4}{5} \times 1 \frac{1}{6} \), let's follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 1 \frac{1}{6} \) can be converted as follows:
\[
1 \frac{1}{6} = 1 + \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6}
\]

### Step 2: Multiply the fractions
Now, multiply \( \frac{4}{5} \) by \( \frac{7}{6} \):
\[
\frac{4}{5} \times \frac{7}{6} = \frac{4 \times 7}{5 \times 6} = \frac{28}{30}
\]

### Step 3: Simplify the fraction
The greatest common divisor (GCD) of 28 and 30 is 2, so we divide both the numerator and the denominator by 2:
\[
\frac{28 \div 2}{30 \div 2} = \frac{14}{15}
\]

### Final Answer
\[
\frac{4}{5} \times 1 \frac{1}{6} = \frac{14}{15}
\]

Would you like more details or have any other questions?

Here are 5 related questions to deepen your understanding:

1. How do you convert any mixed number into an improper fraction?
2. How can you find the greatest common divisor (GCD) to simplify fractions?
3. What happens when multiplying two improper fractions?
4. How do you multiply mixed numbers without converting them to improper fractions?
5. Can you express the answer as a decimal?

**Tip:** Always simplify fractions at the end to get the most reduced form of your answer.

Learn how to multiply the fraction 4/5 by the mixed number 1⅙. This detailed solution covers converting mixed numbers to improper fractions, multiplying fractions, and simplifying the result using the GCD method. Ideal for students in Grades 5-7.

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