We need to evaluate the expression $\frac{5}{12} \times 400$.

1. Problem Description

We need to evaluate the expression $\frac{5}{12} \times 400$.

2. Solution Steps

First, we can multiply the fraction by 400:

$\frac{5}{12} \times 400 = \frac{5 \times 400}{12} = \frac{2000}{12}$.

Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

Both 2000 and 12 are divisible by 4:

$\frac{2000}{12} = \frac{2000 \div 4}{12 \div 4} = \frac{500}{3}$.

Since 500 is not divisible by 3, we can leave the answer as an improper fraction or convert it to a mixed number. To convert $\frac{500}{3}$ to a mixed number, we perform division: $500 \div 3 = 166$ with a remainder of $2$. Therefore, $\frac{500}{3} = 166\frac{2}{3}$.

3. Final Answer

$\frac{500}{3}$ or $166\frac{2}{3}$