To divide the mixed number \(1 \frac{8}{9}\) by the fraction \(\frac{1}{3}\), follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
\[
1 \frac{8}{9} = \frac{9 \times 1 + 8}{9} = \frac{17}{9}
\]

### Step 2: Divide by \(\frac{1}{3}\) by multiplying by the reciprocal.
\[
\frac{17}{9} \div \frac{1}{3} = \frac{17}{9} \times \frac{3}{1} = \frac{17 \times 3}{9 \times 1} = \frac{51}{9}
\]

### Step 3: Simplify the fraction.
\[
\frac{51}{9} = \frac{51 \div 3}{9 \div 3} = \frac{17}{3}
\]

So, \(1 \frac{8}{9} \div \frac{1}{3} = \frac{17}{3}\) or \(5 \frac{2}{3}\) as a mixed number.

Would you like more details or have any questions?

Here are five related questions:
1. What is the result of \(2 \frac{1}{4} \div \frac{1}{2}\)?
2. How do you multiply mixed numbers?
3. What is the reciprocal of \(\frac{3}{7}\)?
4. How do you convert improper fractions to mixed numbers?
5. What is \(1 \frac{8}{9} \times \frac{1}{3}\)?

**Tip:** When dividing fractions, remember to multiply by the reciprocal of the divisor.

Learn how to divide the mixed number 1 8/9 by the fraction 1/3 with a detailed step-by-step solution. This problem covers key concepts in fractions, division of mixed numbers, and multiplying fractions. Suitable for students in Grades 6-8.

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