https://file.aiquickdraw.com/mathbot/file/17261850101537qpcnx26.jpg

The expression shown in the image is:

\[
1 \dfrac{5}{8} \div \dfrac{1}{2}
\]

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 1 \dfrac{5}{8} \) can be written as an improper fraction:
\[
1 \dfrac{5}{8} = \dfrac{8 \times 1 + 5}{8} = \dfrac{13}{8}
\]

### Step 2: Division of fractions
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction:
\[
\dfrac{13}{8} \div \dfrac{1}{2} = \dfrac{13}{8} \times \dfrac{2}{1} = \dfrac{13 \times 2}{8 \times 1} = \dfrac{26}{8}
\]

### Step 3: Simplify the result
Now, simplify the fraction:
\[
\dfrac{26}{8} = \dfrac{13}{4}
\]

So, the answer is \( \dfrac{13}{4} \), or as a mixed number, \( 3 \dfrac{1}{4} \).

Would you like more details on any of these steps?

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Here are some follow-up questions to deepen understanding:
1. How do you convert a mixed number into an improper fraction?
2. Why do we multiply by the reciprocal when dividing fractions?
3. Can you convert \( \dfrac{13}{4} \) into a decimal?
4. What is the difference between multiplying and dividing fractions?
5. How can you simplify \( \dfrac{26}{8} \) step by step?

**Tip:** Always remember to simplify your fractions as a final step to ensure the answer is in its simplest form!

Learn how to divide 1 5/8 by 1/2 in a step-by-step solution. This problem involves converting mixed numbers to improper fractions and applying the rule for dividing fractions.

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