2C. $m$ is a positive fraction such that $m^{2}=\frac{1}{16}+\frac{1}{9}$. Express the value of $m$ in lowest terms.

Step 1 ：Given that $m^{2}=rac{1}{16}+rac{1}{9}$, we first need to add the two fractions together.

Step 2 ：Adding the fractions gives us a sum of approximately 0.1736111111111111.

Step 3 ：Next, we need to find the square root of this sum to find the value of $m$.

Step 4 ：Taking the square root gives us $m$ approximately equal to 0.4166666666666667.

Step 5 ：However, we need to express $m$ in lowest terms as a fraction.

Step 6 ：Converting the decimal to a fraction gives us $m$ as $rac{5}{12}$.

Step 7 ：\(\boxed{\frac{5}{12}}\) is the final answer.