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### 20. Circle the following rational numbers that can be multiplied by four and result in a number greater than four.
For this, we need to check which fractions when multiplied by 4 result in a number greater than 4.

- \( \frac{2}{3} \times 4 = \frac{8}{3} \approx 2.67 \) (less than 4, so not circled)
- \( \frac{10}{3} \times 4 = \frac{40}{3} \approx 13.33 \) (greater than 4, so circled)
- \( \frac{11}{8} \times 4 = \frac{44}{8} = 5.5 \) (greater than 4, so circled)
- \( \frac{8}{15} \times 4 = \frac{32}{15} \approx 2.13 \) (less than 4, so not circled)

The correctly circled fractions should be \( \frac{10}{3} \) and \( \frac{11}{8} \).

### 21. Complete the following with the appropriate inequality symbol:
\[ 4 \times \frac{9}{7} \quad \text{__} \quad 9 \]

- \( 4 \times \frac{9}{7} = \frac{36}{7} \approx 5.14 \)
- \( 5.14 < 9 \)

So the inequality should be \( < \).

### 22. Based on the computations above, describe what happens when multiplying by a fraction results in an increase or decrease to the original number.
- When you multiply by a fraction greater than 1, the result is an increase.
- When you multiply by a fraction less than 1, the result is a decrease.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Multiply \( \frac{3}{4} \times 8 \) and compare it to 8. Is the result greater or smaller?
2. What happens if you multiply a fraction by 0? Will the result always be 0?
3. How does multiplying by a fraction greater than 1 compare to multiplying by a whole number greater than 1?
4. If you multiply \( 2 \times \frac{5}{8} \), is the result larger or smaller than 2?
5. Multiply \( 7 \times \frac{3}{4} \). Will the result increase or decrease?

**Tip**: When multiplying by fractions, keep an eye on whether the fraction is greater or smaller than 1 to predict if the result increases or decreases!

Circle the following rational numbers that can be multiplied by four and result in a number greater than four.

This lesson covers how to multiply rational numbers by whole numbers and determine whether the result is greater than a given value. Suitable for students in Grades 5-7, this problem also teaches how to compare results using inequality symbols.

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