Fractions Using a common donominator to order fractions First, rewrite \( \frac{9}{20} \) and \( \frac{12}{25} \) so that they have a common denominator. Then, use \( < \), \( = \), or \( > \) to order \( \frac{9}{20} \) and \( \frac{12}{25} \). \[ \frac{9}{20}=\frac{\square}{\square} \quad ; \quad \frac{12}{25}=\frac{\square}{\square} \] \( \square \) < \( >\square \) \( \square \) \( \frac{9}{20} \) \( \square \) \[ \frac{12}{25} \]

To compare the fractions \(\frac{9}{20}\) and \(\frac{12}{25}\) using a common denominator, follow these steps: ### 1. Find a Common Denominator The denominators are 20 and 25. - **Factorize the denominators:** - \(20 = 2^2 \times 5\) - \(25 = 5^2\) - **Determine the Least Common Denominator (LCD):** - LCD = \(2^2 \times 5^2 = 4 \times 25 = 100\) ### 2. Rewrite Each Fraction with the Common Denominator Convert each fraction to an equivalent fraction with the denominator of 100. \[ \frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100} \quad ; \quad \frac{12}{25} = \frac{12 \times 4}{25 \times 4} = \frac{48}{100} \] So, the fractions rewritten with a common denominator are: \[ \frac{9}{20} = \frac{45}{100} \quad ; \quad \frac{12}{25} = \frac{48}{100} \] ### 3. Compare the Fractions Now that both fractions have the same denominator, compare their numerators: \[ 45 < 48 \] Therefore, \[ \frac{9}{20} < \frac{12}{25} \] ### Summary \[ \frac{9}{20} = \frac{45}{100} \quad ; \quad \frac{12}{25} = \frac{48}{100} \] \[ 45 < 48 \] \[ \frac{9}{20} < \frac{12}{25} \]