1. **Stating the problem:** Choose the best term from the box (percent, proportion, rate, ratio) to fill in the blanks for questions 1 to 4. 2. **Step 1:** Understand the definitions: - A **percent** is a ratio comparing a number to 100. - A **rate** is a ratio comparing two quantities with different units. - A **proportion** is a statement that two ratios are equal. - A **ratio** is a comparison of two quantities. 3. **Answering questions 1 to 4:** 1. A ________ is a ratio in which the first term is compared to 100. - Answer: **percent** 2. A ratio that relates two quantities with different units of measure is a ________. - Answer: **rate** 3. A statement that two ratios are equal is called a ________. - Answer: **proportion** 4. The relationship “3 students out of 5 students” is an example of a ________. - Answer: **ratio** 5. **Fractions, Decimals, and Percents:** Write each number in two equivalent forms. 6. For 0.29: - As a fraction: $\frac{29}{100}$ - As a percent: $29\%$ 7. For 35%: - As a decimal: $0.35$ - As a fraction: $\frac{35}{100} = \frac{7}{20}$ (simplified) 8. For $\frac{2}{5}$: - As a decimal: $0.4$ - As a percent: $40\%$ 9. **Proportions:** Find the unknown number. 10. For $\frac{4\text{ years}}{x\text{ days}} = \frac{1\text{ year}}{365.25\text{ days}}$: - Cross multiply: $4 \times 365.25 = 1 \times x$ - Calculate: $x = 1461$ days 11. For $\frac{x\text{ miles}}{33,264\text{ feet}} = \frac{1\text{ mile}}{5,280\text{ feet}}$: - Cross multiply: $x \times 5,280 = 33,264 \times 1$ - Calculate: $x = \frac{33,264}{5,280} = \cancel{\frac{33,264}{5,280}} = 6.3$ miles 12. For the cooking magazine: - Proportion: $\frac{5}{12} = \frac{x}{5 \times 12 = 60}$ (total issues in 5 years) - Cross multiply: $12x = 5 \times 60$ - Calculate: $12x = 300$ - Divide: $x = \cancel{\frac{300}{12}} = 25$ **Final answers:** 1. percent 2. rate 3. proportion 4. ratio 5. 0.29 = $\frac{29}{100}$ and 29% 6. 35% = 0.35 and $\frac{7}{20}$ 7. $\frac{2}{5}$ = 0.4 and 40% 8. $x = 1461$ days 9. $x = 6.3$ miles 10. $x = 25$ times