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To solve this problem, we need to use the gear ratio between the two gears. The image shows two gears: one large gear \(A\) and a smaller gear \(B\). The number of teeth on each gear determines their ratio.

### Given information:
- Gear \(A\) has 30 teeth.
- The ratio between gears \(A\) and \(B\) is \(4:5\).

This ratio means that for every 4 rotations of gear \(A\), gear \(B\) rotates 5 times.

The empty box likely asks for the number of teeth on gear \(B\). Since the number of teeth is inversely proportional to the number of rotations, we can use the following relationship:

\[
\frac{\text{Teeth of Gear A}}{\text{Teeth of Gear B}} = \frac{\text{Rotations of Gear B}}{\text{Rotations of Gear A}}
\]

Substituting the given values into the equation:

\[
\frac{30}{\text{Teeth of Gear B}} = \frac{5}{4}
\]

Now, we solve for the number of teeth on gear \(B\):

\[
\text{Teeth of Gear B} = 30 \times \frac{4}{5} = 24
\]

So, the number of teeth on gear \(B\) is 24.

Let me know if you'd like further details!

Here are five related questions for further exploration:
1. What happens if the ratio between the gears was \(5:4\)?
2. How would changing the number of teeth on gear \(B\) affect the rotation ratio?
3. If gear \(B\) had 36 teeth, what would the new rotation ratio be?
4. How do gear ratios affect mechanical advantage in gear systems?
5. What is the impact of friction on gear systems in real-world applications?

**Tip:** Gear ratios are a key concept in machines, especially for adjusting torque and speed between connected gears!

Complete the table with the number of teeth for Gear B given that Gear A has 30 teeth and the ratio between gears A and B is 4:5.

Learn how to calculate the number of teeth for Gear B given Gear A's teeth count and a specific gear ratio. This example demonstrates the application of ratios and inverse proportions for students in Grades 6-8.

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