Question: Spiral Review Problems 8–11: Evaluate each expression. 8. -5 • (-2.4) 9. -7.4 ÷ 10 10. -4/7 ÷ (-2) 11. 4 • (-3/8) 12. Select all of the expressions that have a negative value. A. -11/8 B. -11/8 C. 11/-8 D. -11/-8 E. 11/8

1. **State the problem:** Evaluate each expression from problems 8 to 11 and identify which expressions in problem 12 have negative values. 2. **Recall the rules:** - Multiplying two numbers with the same sign gives a positive result. - Multiplying two numbers with different signs gives a negative result. - Dividing follows the same sign rules as multiplication. - Fractions can be treated as division. 3. **Problem 8:** Evaluate $$-5 \times (-2.4)$$ - Both numbers are negative, so the product is positive. - Calculate $$5 \times 2.4 = 12$$ - Therefore, $$-5 \times (-2.4) = 12$$ 4. **Problem 9:** Evaluate $$-7.4 \div 10$$ - Dividing a negative by a positive gives a negative. - Calculate $$7.4 \div 10 = 0.74$$ - Therefore, $$-7.4 \div 10 = -0.74$$ 5. **Problem 10:** Evaluate $$\frac{-4}{7} \div (-2)$$ - Division of fractions: $$\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}$$ - So, $$\frac{-4}{7} \div (-2) = \frac{-4}{7} \times \frac{1}{-2}$$ - Multiply numerators and denominators: $$\frac{-4 \times 1}{7 \times -2} = \frac{-4}{-14}$$ - Cancel negatives: $$\frac{\cancel{-4}}{\cancel{-14}} = \frac{4}{14}$$ - Simplify fraction: $$\frac{4}{14} = \frac{2}{7}$$ - Therefore, $$\frac{-4}{7} \div (-2) = \frac{2}{7}$$ 6. **Problem 11:** Evaluate $$4 \times \left(-\frac{3}{8}\right)$$ - Multiply numerator: $$4 \times -3 = -12$$ - Denominator remains 8 - So, $$4 \times \left(-\frac{3}{8}\right) = \frac{-12}{8}$$ - Simplify fraction by dividing numerator and denominator by 4: $$\frac{\cancel{-12}}{\cancel{8}} = \frac{-3}{2}$$ - Therefore, $$4 \times \left(-\frac{3}{8}\right) = -\frac{3}{2}$$ 7. **Problem 12:** Identify which expressions have negative values. - A. $$-\frac{11}{8}$$ is negative. - B. $$-\frac{11}{8}$$ is negative (same as A). - C. $$\frac{11}{-8}$$ is negative (negative denominator). - D. $$-\frac{11}{-8}$$ is positive (negative numerator and denominator cancel). - E. $$\frac{11}{8}$$ is positive. **Final answers:** - 8: $$12$$ - 9: $$-0.74$$ - 10: $$\frac{2}{7}$$ - 11: $$-\frac{3}{2}$$ - 12: Expressions A, B, and C have negative values.