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Let's walk through the concepts and problems in the image you've shared.

1. **Variables vs. Units**  
   It explains that a variable represents a measurable quantity in a formula. For example, in the table:  
   - Time is denoted as "t" with units like seconds (s) or hours (h).
   - Distance is "d" in meters (m) or kilometers (km).
   - Speed is "v" in meters per second (m/s) or kilometers per hour (km/h).

2. **Manipulating Formulas**  
   This section guides how to rearrange formulas to solve for different variables. For example:
   - The formula \( A = l \times w \) (area = length × width) can be rearranged to solve for length or width.
     - a) To solve for \( l \), rearrange to \( l = \frac{A}{w} \).
     - b) To solve for \( w \), rearrange to \( w = \frac{A}{l} \).

   Similarly, for speed \( v = \frac{d}{t} \):
   - a) To solve for distance \( d \), rearrange to \( d = v \times t \).
   - b) To solve for time \( t \), rearrange to \( t = \frac{d}{v} \).

3. **Converting Between Units**  
   - Several conversion problems are provided. Here’s how to approach each:
     - a) Convert meters to centimeters: \( 1 \, \text{m} = 100 \, \text{cm} \)
     - b) Convert kilometers to meters: \( 1 \, \text{km} = 1000 \, \text{m} \)
     - c) Convert kilograms to grams: \( 1 \, \text{kg} = 1000 \, \text{g} \)
     - d) Convert milligrams to grams: \( 1 \, \text{g} = 1000 \, \text{mg} \)
     - e) Convert centimeters to meters: \( 1 \, \text{cm} = 0.01 \, \text{m} \)
     - f) Convert grams to kilograms: \( 1 \, \text{kg} = 1000 \, \text{g} \)
     - g) Convert milligrams to kilograms: Combine conversions \( 1 \, \text{kg} = 1000000 \, \text{mg} \)
     - h) Convert meters to millimeters: \( 1 \, \text{m} = 1000 \, \text{mm} \)

   **New: Converting m/s to km/h**  
   - Use the formula to convert \( \text{m/s} \) to \( \text{km/h} \):  
     \( \frac{\text{m}}{\text{s}} \times \frac{1 \, \text{km}}{1000 \, \text{m}} \times \frac{3600 \, \text{s}}{1 \, \text{h}} = \frac{3600}{1000} = 3.6 \, \text{km/h per m/s} \).

Would you like to solve any specific problems from the sheet? Let me know if you need a detailed solution for any of these steps.

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Here are 5 related questions to deepen understanding:
1. How do you rearrange the formula \( F = ma \) to solve for \( a \)?
2. How would you convert 3 km to millimeters?
3. How do you convert 500 m/s to km/h?
4. What is the formula for finding time if distance and speed are known?
5. How do you convert 12.5 kg to milligrams?

**Tip**: Always check units carefully when rearranging formulas to ensure consistent results!

The image contains various problems related to mathematical concepts including variables, units, formula manipulation, and unit conversion.

This page explains key mathematical concepts such as variables vs. units, rearranging formulas for different variables, and converting between units like m to cm, kg to g, and m/s to km/h. Practice solving problems with the formulas provided.

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