The problem is to calculate the value of the expression $\frac{5}{12} \times 400$.

1. Problem Description

The problem is to calculate the value of the expression $\frac{5}{12} \times 400$.

2. Solution Steps

First, we can write the expression as a fraction:

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

Now we can perform the multiplication in the numerator:

$5 \times 400 = 2000$

So the expression becomes:

$\frac{2000}{12}$

Next, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2000 and 12 is

4. Dividing the numerator by 4:

$2000 \div 4 = 500$

Dividing the denominator by 4:

$12 \div 4 = 3$

So the simplified fraction is:

$\frac{500}{3}$

Now we can convert this improper fraction to a mixed number or a decimal.

To find the decimal, we can divide 500 by 3:

$500 \div 3 = 166.666...$

We can round this to two decimal places as $166.67$.

Alternatively, we can express the answer as an improper fraction $\frac{500}{3}$.

3. Final Answer

$\frac{500}{3}$ or $166.67$ (rounded to two decimal places)