1. Problem 8: Find the number halfway between 3000 and 4000. To find the halfway point, calculate the average of 3000 and 4000. $$\text{Halfway} = \frac{3000 + 4000}{2} = \frac{7000}{2} = 3500$$ Answer: The number halfway between 3000 and 4000 is 3500. 2. Problem 9a: Write 24% as a reduced fraction. First, write 24% as a fraction over 100: $$24\% = \frac{24}{100}$$ Now reduce by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 24 and 100 is 4. $$\frac{24 \div 4}{100 \div 4} = \frac{6}{25}$$ Answer: 24% as a reduced fraction is $\frac{6}{25}$. 3. Problem 9b: Reduce $\frac{36}{180}$ using prime factorization. Prime factorize numerator and denominator: $$36 = 2^2 \times 3^2$$ $$180 = 2^2 \times 3^2 \times 5$$ Cancel common factors: $$\frac{36}{180} = \frac{2^2 \times 3^2}{2^2 \times 3^2 \times 5} = \frac{1}{5}$$ Answer: The reduced fraction is $\frac{1}{5}$. 4. Problem 10a: Temperature 102°F is how many degrees above freezing point (32°F). Subtract freezing temperature: $$102 - 32 = 70$$ Answer: 102°F is 70 degrees above freezing. 5. Problem 10b: Temperature 102°F is how many degrees below boiling point (212°F). Subtract current temperature from boiling point: $$212 - 102 = 110$$ Answer: 102°F is 110 degrees below boiling. 6. Problem 10c: Additional information needed to answer parts a and b. We need to know the freezing point (32°F) and boiling point (212°F) of water for these calculations. 7. Problem 11: Write equivalent fractions with denominator 36. a. $\frac{5}{12}$ to denominator 36: Multiply numerator and denominator by $\frac{36}{12} = 3$: $$\frac{5 \times 3}{12 \times 3} = \frac{15}{36}$$ b. $\frac{1}{6}$ to denominator 36: Multiply numerator and denominator by $\frac{36}{6} = 6$: $$\frac{1 \times 6}{6 \times 6} = \frac{6}{36}$$ c. $\frac{7}{9}$ to denominator 36: Multiply numerator and denominator by $\frac{36}{9} = 4$: $$\frac{7 \times 4}{9 \times 4} = \frac{28}{36}$$ d. Property used is the equivalence of fractions: multiplying numerator and denominator by the same nonzero number does not change the value. Answer: a. $\frac{15}{36}$ b. $\frac{6}{36}$ c. $\frac{28}{36}$