1. Reduce $\frac{36}{63}$ to lowest terms. Step 1: Find the greatest common divisor (GCD) of 36 and 63. Step 2: $\text{GCD}(36,63) = 9$ Step 3: Divide numerator and denominator by 9: $$\frac{36}{63} = \frac{\cancel{9} \times 4}{\cancel{9} \times 7} = \frac{4}{7}$$ Answer: $\frac{4}{7}$ 2. Rename $7 \frac{4}{9}$ as an improper fraction. Step 1: Multiply the whole number by the denominator and add the numerator: $$7 \times 9 + 4 = 63 + 4 = 67$$ Step 2: Write as improper fraction: $$\frac{67}{9}$$ Answer: $\frac{67}{9}$ 3. Rename $-\frac{112}{12}$ as a mixed number. Step 1: Divide 112 by 12: $$112 \div 12 = 9 \text{ remainder } 4$$ Step 2: Write as mixed number with negative sign: $$-9 \frac{4}{12}$$ Step 3: Simplify fraction $\frac{4}{12}$ by dividing numerator and denominator by 4: $$\frac{4}{12} = \frac{\cancel{4} \times 1}{\cancel{4} \times 3} = \frac{1}{3}$$ Answer: $-9 \frac{1}{3}$ 4. Evaluate the expression $\frac{5x}{7y}$ if $x = -2$ and $y = 3$. Step 1: Substitute values: $$\frac{5 \times (-2)}{7 \times 3} = \frac{-10}{21}$$ Answer: $-\frac{10}{21}$ 5. Compare each pair of fractions by using $<$, $=$, or $>$. a. Compare $\frac{15}{24}$ and $\frac{20}{32}$. Step 1: Simplify both fractions: $$\frac{15}{24} = \frac{\cancel{3} \times 5}{\cancel{3} \times 8} = \frac{5}{8}$$ $$\frac{20}{32} = \frac{\cancel{4} \times 5}{\cancel{4} \times 8} = \frac{5}{8}$$ Step 2: Since both are $\frac{5}{8}$, they are equal. Answer: $=$ b. Compare $-\frac{3}{4}$ and $-\frac{13}{15}$. Step 1: Find common denominator $4 \times 15 = 60$. Step 2: Convert fractions: $$-\frac{3}{4} = -\frac{3 \times 15}{4 \times 15} = -\frac{45}{60}$$ $$-\frac{13}{15} = -\frac{13 \times 4}{15 \times 4} = -\frac{52}{60}$$ Step 3: Compare numerators $-45$ and $-52$; since $-45 > -52$, $$-\frac{3}{4} > -\frac{13}{15}$$ Answer: $>$