We need to calculate the value of the expression $\frac{5}{12} \times 400$.

1. Problem Description

We need to calculate the value of the expression $\frac{5}{12} \times 400$.

2. Solution Steps

First, we can rewrite the expression as:

$\frac{5 \times 400}{12}$

Now, multiply 5 by 400:

$5 \times 400 = 2000$

So, the expression becomes:

$\frac{2000}{12}$

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor.

First, divide both the numerator and denominator by 4:

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

Now, we can express the fraction as a mixed number or a decimal. Let's find the decimal representation.

Divide 500 by 3:

$500 \div 3 = 166.666...$ which can be written as $166\frac{2}{3}$.

3. Final Answer

$\frac{5}{12} \times 400 = \frac{500}{3} = 166\frac{2}{3} \approx 166.67$