Question

use the benchmark \\(\frac{1}{2}\\) to compare \\(\frac{3}{5}\\) and \\(\frac{4}{9}\\). first, compare each fraction to \\(\frac{1}{2}\\). \\(\frac{3}{5}\\) is? \\(\frac{1}{2}\\). \\(\frac{4}{9}\\) is? \\(\frac{1}{2}\\).

Explanation:

Step1: Compare $\frac{3}{5}$ and $\frac{1}{2}$

To compare $\frac{3}{5}$ and $\frac{1}{2}$, find a common denominator. The common denominator of 5 and 2 is 10. Convert both fractions: $\frac{3}{5} = \frac{3\times2}{5\times2} = \frac{6}{10}$ and $\frac{1}{2} = \frac{1\times5}{2\times5} = \frac{5}{10}$. Since $\frac{6}{10} > \frac{5}{10}$, $\frac{3}{5} > \frac{1}{2}$.

Step2: Compare $\frac{4}{9}$ and $\frac{1}{2}$

Find a common denominator for 9 and 2, which is 18. Convert both fractions: $\frac{4}{9} = \frac{4\times2}{9\times2} = \frac{8}{18}$ and $\frac{1}{2} = \frac{1\times9}{2\times9} = \frac{9}{18}$. Since $\frac{8}{18} < \frac{9}{18}$, $\frac{4}{9} < \frac{1}{2}$.

Answer:

$\frac{3}{5}$ is greater than $\frac{1}{2}$; $\frac{4}{9}$ is less than $\frac{1}{2}$