Let's analyze and solve the problems in the image you uploaded:

1. Problem 1:
   $6 \text{ dm} + 3 \text{ cm} + 7 \text{ mm} =$ $637 \text{ mm}$

   To solve this:

   • $6 \text{ dm} = 600 \text{ mm}$ (since 1 dm = 100 mm)
   • $3 \text{ cm} = 30 \text{ mm}$ (since 1 cm = 10 mm)
   • $7 \text{ mm}$ remains as it is.

   Therefore, $600 \text{ mm} + 30 \text{ mm} + 7 \text{ mm} = 637 \text{ mm}$.
   The answer is correct.

2. Problem 2:
   $9 \text{ km} + 14 \text{ hm} + 450 \text{ dm} = 14900 \text{ m}$

   To solve this:

   • $9 \text{ km} = 9000 \text{ m}$ (since 1 km = 1000 m)
   • $14 \text{ hm} = 1400 \text{ m}$ (since 1 hm = 100 m)
   • $450 \text{ dm} = 45 \text{ m}$ (since 1 dm = 0.1 m)

   Therefore, $9000 \text{ m} + 1400 \text{ m} + 45 \text{ m} = 10445 \text{ m}$.
   The expected answer $14900 \text{ m}$ does not match the correct calculation, so the input answer is incorrect.

3. Problem 3:
   $75.6 \text{ cm} + 4.5 \text{ dm} - 5.4 \text{ cm} =$

   To solve this:

   • $75.6 \text{ cm}$ remains as it is.
   • $4.5 \text{ dm} = 45 \text{ cm}$ (since 1 dm = 10 cm)
   • Subtract $5.4 \text{ cm}$.

   Therefore, $75.6 \text{ cm} + 45 \text{ cm} - 5.4 \text{ cm} = 115.2 \text{ cm}$.
   The answer $115.2 \text{ cm}$ should be entered.

4. Problem 4:
   $47.5 \text{ hm} + 4 \text{ km} + 52.5 \text{ hm} = 14 \text{ km}$

   To solve this:

   • $47.5 \text{ hm} = 4.75 \text{ km}$
   • $4 \text{ km}$ remains as it is.
   • $52.5 \text{ hm} = 5.25 \text{ km}$

   Therefore, $4.75 \text{ km} + 4 \text{ km} + 5.25 \text{ km} = 14 \text{ km}$.
   The answer is correct.

Would you like any more details or have any questions?

Here are some related questions to explore:

1. How do you convert between different units of length, like meters to kilometers?
2. Why is it important to keep consistent units when adding or subtracting measurements?
3. What are common mistakes to avoid when performing unit conversions?
4. How can you quickly verify the correctness of unit conversion?
5. Can you think of real-life situations where these conversions are useful?

Tip: Always ensure that all terms are converted to the same unit before performing any arithmetic operations.