Amanita, let's carefully solve the problem step by step.

Step 1: Understanding the Problem

The question asks: "Does this fraction make sense?" This means we need to check if the denominator is not zero, because division by zero is not allowed in mathematics.

The fraction is:

$\frac{340.3 + (2.1 \div 2 - 1.8) \cdot 0.4}{1.4 \div 0.02 - 2}$

Step 2: Plan

1. Calculate the denominator: $1.4 \div 0.02 - 2$.
2. Check if the denominator is zero. If it is, the fraction does not make sense.
3. If the denominator is not zero, the fraction makes sense.

Let's start by calculating the denominator. Amanita, after calculating the denominator, we get:

$$1.4 \div 0.02 - 2 = 68$$

Since the denominator is 68, which is not zero, the fraction does make sense. This means you can calculate its value, and it is a valid mathematical expression.