Math teacher explaining fraction problem-solving on a whiteboard.

Let's solve the problem shown on the whiteboard:

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Problem:

> In a herd of horses, 4 are speckled and the rest are not. Also, $ \frac{7}{9} $ of the herd are not speckled. How many horses are in the herd?

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Step-by-Step Solution:

We are told:
- 4 horses are speckled.
- $ \frac{7}{9} $ of the herd are not speckled.

That means the remaining fraction of the herd that are speckled is:
$$
1 - \frac{7}{9} = \frac{2}{9}
$$

So, $ \frac{2}{9} $ of the total herd equals the 4 speckled horses.

Let’s let $ x $ be the total number of horses in the herd.

Then:
$$
\frac{2}{9}x = 4
$$

Now solve for $ x $:
$$
x = 4 \div \frac{2}{9} = 4 \times \frac{9}{2} = \frac{36}{2} = 18
$$

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✔ Answer:

There are 18 horses in the herd.

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Check:

- $ \frac{7}{9} $ of 18 = $ \frac{7}{9} \times 18 = 14 $ — not speckled
- So, $ 18 - 14 = 4 $ — speckled → matches the given info.

✔️ Correct!

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Let me know if you'd like help with the other problems on the board too!