Question: User: Jenny compares the lengths of two pencils.
• The longer pencil is 6 1/2 inches in length.
• The shorter pencil is 4 1/3 inches in length.
What is the ratio of the longer length to the shorter length?
1. **State the problem:** We need to find the ratio of the longer pencil length to the shorter pencil length.
2. **Convert mixed numbers to improper fractions:**
- Longer pencil: $6 \frac{1}{2} = \frac{13}{2}$ inches
- Shorter pencil: $4 \frac{1}{3} = \frac{13}{3}$ inches
3. **Write the ratio as a fraction:**
$$\text{Ratio} = \frac{\text{Longer length}}{\text{Shorter length}} = \frac{\frac{13}{2}}{\frac{13}{3}}$$
4. **Divide the fractions by multiplying by the reciprocal:**
$$\frac{13}{2} \times \frac{3}{13}$$
5. **Cancel common factors:**
$$\frac{\cancel{13}}{2} \times \frac{3}{\cancel{13}} = \frac{3}{2}$$
6. **Interpret the result:** The ratio of the longer pencil to the shorter pencil is $\frac{3}{2}$ or 3:2.
**Final answer:** The ratio of the longer pencil length to the shorter pencil length is $\boxed{\frac{3}{2}}$ or 3:2.