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.

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!