write two mixed numbers between 3 and 4 that have a product between 9 and 12
Consider 2 decimal numbers which are close to 3, like 3.1 and 3.2 .
They are both larger than 3, so their multiplication will be larger than 9. We keep them close to 3 so that the product is not larger than 12.
We may still fail, but we can check.
Now let's write the 2 decimal numbers as mixed numbers.
3.1 is \(3+ \frac{1}{10}\), which is \(3 \frac{1}{10}\)
Similarly 3.2 is \(3 \frac{2}{10}\).
The multiplication of these 2 numbers is:
\((3+ \frac{1}{10})\cdot (3+ \frac{2}{10}) =9+ \frac{6}{10}+ \frac{3}{10}+ \frac{2}{100}=9+0.6+0.3+0.02=9.92\)
Answer: \(3 \frac{1}{10}\), \(3 \frac{2}{10}\)