To solve the division of the mixed number \(15 \frac{3}{8}\) by \( \frac{1}{2}\), follow these steps:

### Step 1: Convert the Mixed Number to an Improper Fraction
First, convert \(15 \frac{3}{8}\) into an improper fraction.
\[
15 \frac{3}{8} = \frac{(15 \times 8) + 3}{8} = \frac{120 + 3}{8} = \frac{123}{8}
\]

### Step 2: Division of Fractions
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, divide \(\frac{123}{8}\) by \(\frac{1}{2}\) by multiplying by the reciprocal of \(\frac{1}{2}\), which is \(2\).
\[
\frac{123}{8} \div \frac{1}{2} = \frac{123}{8} \times 2 = \frac{123 \times 2}{8} = \frac{246}{8}
\]

### Step 3: Simplify the Fraction
Now, simplify \(\frac{246}{8}\).
\[
\frac{246}{8} = \frac{123}{4}
\]

### Step 4: Convert Back to a Mixed Number
Finally, convert \(\frac{123}{4}\) back into a mixed number.
\[
\frac{123}{4} = 30 \frac{3}{4}
\]

So, \(15 \frac{3}{8} \div \frac{1}{2} = 30 \frac{3}{4}\).

Would you like more details on any part of the process? Here are some related problems you might find useful:

1. What is \(8 \frac{5}{6} \div \frac{3}{4}\)?
2. How do you multiply \(12 \frac{1}{4}\) by \(\frac{2}{3}\)?
3. What is the result of \( \frac{15}{7} \div \frac{3}{2}\)?
4. How do you simplify the fraction \(\frac{256}{64}\)?
5. Convert \(20 \frac{7}{10}\) to an improper fraction.

**Tip:** Remember, dividing by a fraction is the same as multiplying by its reciprocal!

Learn how to solve the division problem 15 3/8 divided by 1/2 step-by-step. Convert mixed numbers to improper fractions, divide fractions by multiplying by the reciprocal, and simplify the result. Suitable for grades 6-8, this problem covers key concepts in fractions and division of fractions.

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