20. A stop sign has the shape of an of of an eight-sided polygon? 21. There were 15 boys and 12 girls in the class. a. What fraction of the class was made up of girls? b. What was the ratio of boys to girls in the class? 22. Verify Instead of dividing \( 4 \frac{1}{2} \) by \( 1 \frac{1}{2} \), Carla doubled br \( { }^{(43)} \) dividing mentally. What was Carla's mental division pr

Sure, let's address each of your questions one by one. --- ### **20. A stop sign has the shape of an eight-sided polygon?** **Answer:** Yes, a stop sign typically has the shape of an **octagon**, which is an eight-sided polygon. --- ### **21. There were 15 boys and 12 girls in the class.** **a. What fraction of the class was made up of girls?** **Solution:** - **Total number of students** = Number of boys + Number of girls = 15 boys + 12 girls = **27 students** - **Fraction of girls in the class** = Number of girls / Total number of students = 12 / 27 = Simplify by dividing numerator and denominator by 3 = **4/9** **Answer:** The fraction of the class made up of girls is **4⁄9**. --- **b. What was the ratio of boys to girls in the class?** **Solution:** - **Number of boys** = 15 - **Number of girls** = 12 - **Ratio of boys to girls** = 15 : 12 = Simplify by dividing both numbers by 3 = **5 : 4** **Answer:** The ratio of boys to girls in the class is **5 : 4**. --- ### **22. Verify Instead of dividing \( 4 \frac{1}{2} \) by \( 1 \frac{1}{2} \), Carla doubled before dividing mentally. What was Carla's mental division problem?** **Understanding the Question:** Carla was supposed to divide \( 4 \frac{1}{2} \) by \( 1 \frac{1}{2} \). Instead of performing this division directly, she **doubled** both the dividend and the divisor before dividing. **Step-by-Step Solution:** 1. **Original Division Problem:** \( 4 \frac{1}{2} \div 1 \frac{1}{2} \) 2. **Convert Mixed Numbers to Improper Fractions:** - \( 4 \frac{1}{2} = \frac{9}{2} \) - \( 1 \frac{1}{2} = \frac{3}{2} \) 3. **Carla's Approach:** She **doubled** both the numerator and the denominator: - New Dividend: \( \frac{9}{2} \times 2 = 9 \) - New Divisor: \( \frac{3}{2} \times 2 = 3 \) 4. **Carla's Mental Division Problem:** \( 9 \div 3 \) 5. **Solution to Carla's Problem:** \( 9 \div 3 = 3 \) **Verification through Original Division:** - \( 4 \frac{1}{2} \div 1 \frac{1}{2} = \frac{9}{2} \div \frac{3}{2} = \frac{9}{2} \times \frac{2}{3} = \frac{9 \times 2}{2 \times 3} = \frac{18}{6} = 3 \) **Answer:** Carla's mental division problem was **9 ÷ 3**, and the result is **3**. --- If you have any more questions or need further clarification, feel free to ask!