Name: Teacher : Ratios and Rates Express each ratio as a fraction in the simplest form. \begin{tabular}{ll} 1) 20 quarts to 28 quarts \\ 3) 2 pennies to 4 pennies & 2) 4 blue cars out of 10 cars \\ 5) 8 gallons to 22 gallons & 4) 20 cups to 36 cups \\ 7) 33 miles out of 36 miles & 6) 28 beetles out of 63 insects \\ \hline\end{tabular}

To express each ratio as a fraction in the simplest form, we will follow these steps: 1. Write the ratio as a fraction. 2. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. 3. Divide both the numerator and denominator by their GCD. Let's go through each ratio step by step. 1) **20 quarts to 28 quarts**: - Write as a fraction: \(\frac{20}{28}\) - GCD of 20 and 28 is 4. - Simplify: \(\frac{20 \div 4}{28 \div 4} = \frac{5}{7}\) 2) **4 blue cars out of 10 cars**: - Write as a fraction: \(\frac{4}{10}\) - GCD of 4 and 10 is 2. - Simplify: \(\frac{4 \div 2}{10 \div 2} = \frac{2}{5}\) 3) **2 pennies to 4 pennies**: - Write as a fraction: \(\frac{2}{4}\) - GCD of 2 and 4 is 2. - Simplify: \(\frac{2 \div 2}{4 \div 2} = \frac{1}{2}\) 4) **20 cups to 36 cups**: - Write as a fraction: \(\frac{20}{36}\) - GCD of 20 and 36 is 4. - Simplify: \(\frac{20 \div 4}{36 \div 4} = \frac{5}{9}\) 5) **8 gallons to 22 gallons**: - Write as a fraction: \(\frac{8}{22}\) - GCD of 8 and 22 is 2. - Simplify: \(\frac{8 \div 2}{22 \div 2} = \frac{4}{11}\) 6) **28 beetles out of 63 insects**: - Write as a fraction: \(\frac{28}{63}\) - GCD of 28 and 63 is 7. - Simplify: \(\frac{28 \div 7}{63 \div 7} = \frac{4}{9}\) 7) **33 miles out of 36 miles**: - Write as a fraction: \(\frac{33}{36}\) - GCD of 33 and 36 is 3. - Simplify: \(\frac{33 \div 3}{36 \div 3} = \frac{11}{12}\) Now, let's summarize the results: 1) \( \frac{5}{7} \) 2) \( \frac{2}{5} \) 3) \( \frac{1}{2} \) 4) \( \frac{5}{9} \) 5) \( \frac{4}{11} \) 6) \( \frac{4}{9} \) 7) \( \frac{11}{12} \)